World!Of Numbers |
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[ February 2, 2011 ] [ Last Update January 21, 2013 ] [ November 2011 ] Our Beloved Prof V.K Doraswamy - A Memoir (†) - goto memoir On the topic Sum Of Powers (WON plate 178), I had stated that" With the liberty to use squares, cubes... All numbers above 23 are either powers or sums of powers ". Enclosed is a sheet to substantiate this statement, which may be of interest to you and other Math lovers.
It is possible to express EVERY NUMBER above 23, Evolved readers can think of devising suitable Java script
From B.S. Rangaswamy [ November 19, 2011 ] A few days back, I came across a moving vehicle bearing reg. no '9441'.
Thus it was possible to arrive also at 2 tier results. This is to illustrate [ November 2011 ]
With due regards to Mr Albert H Beiler, I have attempted to find
A. Reverse of ninedigital squares (30 nos)
No pandigital cubes exist in 10 digit numbers. Only 6 cubes with
E. Reverse of elevendigital cubes (6 nos)
Enclosing detailed sums of powers for all the above combinations, |
A. Reverse Ninedigital Squares as Sum of Powers | |||||
---|---|---|---|---|---|
Sl.No | Power | Ninedigital Square |
| Sum Of Powers | |
1 | 234392 | 549386721 | 127683945 | 112982 + 1502 + 1292 | |
2 | 271292 | 735982641 | 146289537 | 120952 + 29 | |
3 | 196292 | 385297641 | 146792583 | 121132 + 373 + 1312 | |
4 | 230192 | 529874361 | 163478925 | 127812 + 3422 + 203 | |
5 | 156812 | 245893761 | 167398542 | 129382 + 732 + 372 | |
6 | 195692 | 382945761 | 167549283 | 129412 + 2812 + 292 | |
7 | 264092 | 697435281 | 182534796 | 135022 + 4342 + 2062 | |
8 | 244412 | 597362481 | 184263795 | 135712 + 2752 + 1272 | |
9 | 250592 | 627953481 | 184359726 | 135772 + 1462 + 592 | |
10 | 259412 | 672935481 | 184539276 | 455 + 65 + 153 | |
11 | 255722 | 653927184 | 481729356 | 219462 + 3142 + 622 | |
12 | 180722 | 326597184 | 481795623 | 7833 + 11282 + 783 | |
13 | 231782 | 537219684 | 486912735 | 220662 + 153 + 103 + 22 | |
14 | 291062 | 847159236 | 632951748 | 251582 + 1532 + 153 | |
15 | 290342 | 842973156 | 651379248 | 255162 + 5242 + 144 | |
16 | 303842 | 923187456 | 654781329 | 255872 + 2942 + 182 | |
17 | 203162 | 412739856 | 658937214 | 256672 + 3772 + 142 | |
18 | 242762 | 589324176 | 671423985 | 259112 + 1802 + 1082 | |
19 | 118262 | 139854276 | 672458931 | 259312 + 2032 + 312 | |
20 | 146762 | 215384976 | 679483512 | 260582 + 6422 + 2282 | |
21 | 193772 | 375468129 | 921864573 | 303622 + 1022 + 55 | |
22 | 190232 | 361874529 | 925478163 | 304172 + 5252 + 932 | |
23 | 272732 | 743816529 | 925618347 | 304232 + 2372 + 572 | |
24 | 248072 | 615387249 | 942783516 | 306962 + 803 + 303 + 102 | |
25 | 125432 | 157326849 | 948623751 | 307992 + 2012 + 702 + 72 | |
26 | 242372 | 587432169 | 961234785 | 310002 + 224 + 232 | |
27 | 159632 | 254817369 | 963718452 | 310342 + 7642 + 1602 | |
28 | 123632 | 152843769 | 967348251 | 311012 + 2732 + 392 | |
29 | 228872 | 523814769 | 967418325 | 9893 + 66 + 104 | |
30 | 267332 | 714653289 | 982356417 | 313422 + 1872 + 222 |
|
B. Reverse Pandigital Squares as Sum of Powers | |||||
---|---|---|---|---|---|
Sl.No | Power | Pandigital Square |
| Sum Of Powers | |
1 | 630512 | 3975428601 | 1068245793 | 326842 + 412 + 28 | |
2 | 803612 | 6457890321 | 1230987546 | 350852 + 1392 + 104 + 103 | |
3 | 876392 | 7680594321 | 1234950867 | 351412 + 2452 + 312 | |
4 | 629612 | 3964087521 | 1257804693 | 354632 + 3902 + 1682 | |
5 | 626792 | 3928657041 | 1407568293 | 375132 + 5802 + 822 | |
6 | 573212 | 3285697041 | 1407965823 | 375222 + 2552 + 172 + 52 | |
7 | 890792 | 7935068241 | 1428605397 | 377932 + 5422 + 282 | |
8 | 631292 | 3985270641 | 1460725893 | 382172 + 4202 + 1022 | |
9 | 726212 | 5273809641 | 1469083725 | 383262 + 3402 + 2932 | |
10 | 977792 | 9560732841 | 1482370659 | 384972 + 5692 + 1672 | |
11 | 555812 | 3089247561 | 1657429803 | 407092 + 4512 + 612 | |
12 | 839192 | 7042398561 | 1658932407 | 407292 + 2792 + 552 + 102 | |
13 | 687812 | 4730825961 | 1695280374 | 411732 + 2512 + 382 | |
14 | 757592 | 5739426081 | 1806249375 | 424972 + 5042 + 152 + 53 or 715 + 11002 + 304 + 24 + 23 | |
15 | 988022 | 9761835204 | 4025381679 | 634412 + 7832 + 902 + 32 | |
16 | 901982 | 8135679204 | 4029765318 | 634802 + 2332 + 54 + 22 | |
17 | 912482 | 8326197504 | 4057916238 | 637002 + 4672 + 902 + 72 | |
18 | 439022 | 1927385604 | 4065837291 | 637632 + 3412 + 292 | |
19 | 967022 | 9351276804 | 4086721539 | 639272 + 2272 + 912 + 202 | |
20 | 846482 | 7165283904 | 4093825617 | 639832 + 64 + 25 | |
21 | 488522 | 2386517904 | 4097156832 | 640082 + 3482 + 1082 | |
22 | 565322 | 3195867024 | 4207685913 | 648632 + 6622 + 1702 + 104 | |
23 | 761822 | 5803697124 | 4217963085 | 649432 + 5442 + 2702 + 103 | |
24 | 549182 | 3015986724 | 4276895103 | 653972 + 3552 + 372 + 102 | |
25 | 780722 | 6095237184 | 4817325906 | 694062 + 3532 + 902 + 192 | |
26 | 812222 | 6597013284 | 4823107956 | 694482 + 2442 + 1542 | |
27 | 351722 | 1237069584 | 4859607321 | 697102 + 3112 + 1602 + 302 | |
28 | 387722 | 1503267984 | 4897623051 | 699832 + 74 + 192 | |
29 | 891452 | 7946831025 | 5201386497 | 721172 + 6182 + 3782 | |
30 | 661052 | 4369871025 | 5201789634 | 721222 + 4452 + 902 + 54 | |
31 | 946952 | 8967143025 | 5203417698 | 721332 + 4972 + 103 | |
32 | 980552 | 9614783025 | 5203874169 | 721372 + 3502 + 702 | |
33 | 819452 | 6714983025 | 5203894176 | 721382 + 542 + 63 | |
34 | 893552 | 7984316025 | 5206134897 | 721512 + 5642 + 2002 + 104 | |
35 | 916052 | 8391476025 | 5206741938 | 721562 + 5012 + 512 | |
36 | 584552 | 3416987025 | 5207896143 | 721652 + 3302 + 32 + 32 | |
37 | 405452 | 1643897025 | 5207983461 | 721652 + 583 + 210 + 102 | |
38 | 804452 | 6471398025 | 5208931746 | 721722 + 3292 + 1612 | |
39 | 379052 | 1436789025 | 5209876341 | 721792 + 2302 + 1202 + 103 | |
40 | 615752 | 3791480625 | 5260841973 | 725292 + 6042 + 1462 | |
41 | 773462 | 5982403716 | 6173042895 | 785652 + 7492 + 1502 + 132 | |
42 | 951542 | 9054283716 | 6173824509 | 785732 + 3182 + 842 | |
43 | 585542 | 3428570916 | 6190758243 | 786792 + 5212 + 3192 | |
44 | 554462 | 3074258916 | 6198524703 | 787272 + 7152 + 2702 + 72 | |
45 | 507062 | 2571098436 | 6348901752 | 796782 + 683 + 602 + 62 | |
46 | 427442 | 1827049536 | 6359407281 | 797442 + 234 + 1482 | |
47 | 901442 | 8125940736 | 6370495218 | 798132 + 703 + 1932 | |
48 | 331442 | 1098524736 | 6374258901 | 798382 + 3562 + 1612 | |
49 | 440162 | 1937408256 | 6528047391 | 807952 + 4452 + 1302 + 212 | |
50 | 609842 | 3719048256 | 6528409173 | 807982 + 2872 + 104 | |
51 | 990662 | 9814072356 | 6532704189 | 808252 + 1502 + 103 + 26 | |
52 | 618662 | 3827401956 | 6591047283 | 811852 + 2032 + 432 | |
53 | 656342 | 4307821956 | 6591287034 | 925 + 5112 + 4592 | |
54 | 662762 | 4392508176 | 6718052934 | 819632 + 3422 + 512 | |
55 | 456242 | 2081549376 | 6739451802 | 820912 + 6802 + 2392 | |
56 | 555242 | 3082914576 | 6754192803 | 821832 + 3832 + 54 | |
57 | 539762 | 2913408576 | 6758043192 | 822062 + 603 + 36 + 33 | |
58 | 556262 | 3094251876 | 6781524903 | 823502 + 37 + 63 | |
60 | 493142 | 2431870596 | 6950781342 | 833702 + 4712 + 512 | |
61 | 922142 | 8503421796 | 6971243058 | 834912 + 7042 + 192 | |
62 | 322862 | 1042385796 | 6975832401 | 835212 + 2682 + 562 | |
63 | 393362 | 1547320896 | 6980237451 | 835472 + 3692 + 34 | |
64 | 784532 | 6145873209 | 9023785416 | 949922 + 4242 + 503 + 242 | |
65 | 760472 | 5783146209 | 9026413875 | 950072 + 2852 + 512 | |
66 | 901532 | 8127563409 | 9043657218 | 950972 + 3602 + 2972 | |
67 | 594032 | 3528716409 | 9046178253 | 951102 + 4932 + 1522 | |
68 | 853532 | 7285134609 | 9064315827 | 952052 + 4892 + 2912 | |
69 | 358532 | 1285437609 | 9067345821 | 952222 + 3412 + 28 | |
70 | 391472 | 1532487609 | 9067842351 | 952232 + 5812 + 2902 + 312 | |
71 | 493532 | 2435718609 | 9068175342 | 952262 + 4292 + 152 | |
72 | 858032 | 7362154809 | 9084512637 | 953122 + 3472 + 1222 | |
73 | 886232 | 7854036129 | 9216304587 | 960012 + 3352 + 192 | |
74 | 860732 | 7408561329 | 9231658047 | 960812 + 2692 + 303 + 53 | |
75 | 676772 | 4580176329 | 9236710854 | 961072 + 3942 + 132 | |
76 | 895232 | 8014367529 | 9257634108 | 962102 + 11002 + 2382 + 582 | |
77 | 857432 | 7351862049 | 9402681537 | 969672 + 2722 + 922 | |
78 | 357572 | 1278563049 | 9403658721 | 969722 + 2972 + 123 | |
79 | 320432 | 1026753849 | 9483576201 | 973822 + 234 + 2062 | |
80 | 687632 | 4728350169 | 9610538274 | 980332 + 2632 + 24 | |
81 | 695132 | 4832057169 | 9617502384 | 980682 + 4122 + 24 | |
82 | 353372 | 1248703569 | 9653078421 | 982502 + 1202 + 392 | |
83 | 465872 | 2170348569 | 9658430712 | 982762 + 5062 + 502 | |
84 | 584132 | 3412078569 | 9658702143 | 982772 + 5752 + 502 + 172 | |
85 | 656372 | 4308215769 | 9675128034 | 983612 + 3972 + 2902 + 22 | |
86 | 455672 | 2076351489 | 9841536702 | 992032 + 4822 + 2632 | |
87 | 714332 | 5102673489 | 9843762015 | 992152 + 3712 + 902 + 72 |
|
C. Palindromic Twin Ninedigitals as Sum of Powers | |||
---|---|---|---|
Sl.No | Power | Palindromes - 18 digits Ninedgt. Sq._Reversed Ninedgt. Sq. | Sum Of Powers |
1 | 118262 | 139854276_672458931 | 3739709552 + 385852 + 2092 + 103 |
2 | 123632 | 152843769_967348251 | 3909523882 + 168652 + 1292 + 292 |
3 | 125432 | 157326849_948623751 | 3966444872 + 296832 + 1732 + 1422 |
4 | 146762 | 215384976_679483512 | 4640958702 + 113242 + 4402 + 62 |
5 | 156812 | 245893761_167398542 | 4958767602 + 77002 + 213 + 412 |
6 | 159632 | 254817369_963718452 | 5047943832 + 292452 + 3032 + 772 |
7 | 180722 | 326597184_481795623 | 5714868192 + 138222 + 932 + 232 |
8 | 190232 | 361874529_925478163 | 6015600802 + 87102 + 742 + 37 |
9 | 193772 | 375468129_921864573 | 6127545422 + 343542 + 1672 + 982 |
10 | 195692 | 382945761_167549283 | 6188261152 + 236972 + 852 + 210 |
11 | 196292 | 385297641_146792583 | 6207234822 + 63692 + 1372 + 732 |
12 | 203162 | 412739856_658937214 | 6424483292 + 349862 + 1572 + 27 |
13 | 228872 | 523814769_967418325 | 7237504882 + 329702 + 3912 + 802 |
14 | 230192 | 529874361_163478925 | 7279246942 + 320702 + 172 + 102 |
15 | 231782 | 537219684_486912735 | 7329527152 + 453952 + 5662 + 1232 |
16 | 234392 | 549386721_127683945 | 7412062602 + 355592 + 1702 + 1582 |
17 | 242372 | 587432169_961234785 | 7664412372 + 136802 + 462 + 102 |
18 | 242762 | 589324176_671423985 | 7676745252 + 183682 + 2062 + 1502 |
19 | 244412 | 597362481_184263795 | 7728922832 + 79562 + 1172 + 34 |
20 | 248072 | 615387249_942783516 | 7844662192 + 345052 + 1732 + 512 |
21 | 250592 | 627953481_184359726 | 7924351582 + 393682 + 1832 + 432 |
22 | 255722 | 653927184_481729356 | 8086576432 + 299872 + 4032 + 1772 |
23 | 259412 | 672935481_184539276 | 8203264472 + 392012 + 3152 + 2792 |
24 | 264092 | 697435281_182534796 | 8351259072 + 252972 + 1532 + 232 |
25 | 267332 | 714653289_982356417 | 8453716872 + 283042 + 1162 + 242 |
26 | 271292 | 735982641_146289537 | 8578943062 + 296462 + 4272 + 28 |
27 | 272732 | 743816529_925618347 | 8624479852 + 556312 + 4752 + 1562 |
28 | 290342 | 842973156-651379248 | 9181356962 + 195402 + 4042 + 24 |
29 | 291062 | 847159236_632951748 | 9204125362 + 143822 + 3682 + 1522 |
30 | 303842 | 923187456_654781329 | 9608264442 + 341322 + 3002 + 1132 |
|
D. Palindromic Twin Pandigitals as Sum of Powers | |||
---|---|---|---|
Sl.No | Power | Palindromes - 20 digits Reversed Pandgt. Sq._Pandgt. Sq. | Sum Of Powers |
1 | 630512 | 1068245793_3975428601 | 32684029632 + 736742 + 5302 + 3302 + 342 |
2 | 803612 | 1230987546_6457890321 | 35085432112 + 548062 + 422 + 202 |
3 | 876392 | 1234950867_7680594321 | 35141867732 + 463942 + 1662 + 104 |
4 | 629612 | 1257804693_3964087521 | 35465542332 + 797082 + 7082 + 522 |
5 | 626792 | 1407568293_3928657041 | 37517573122 + 760452 + 5342 + 2542 |
6 | 573212 | 1407965823_3285697041 | 37522870672 + 104982 + 1222 + 1082 |
7 | 890792 | 1428605397_7935068241 | 37796896652 + 1192762 + 6562 + 2482 |
8 | 631292 | 1460725893_3985270641 | 38219443902 + 1171872 + 622 + 123 |
9 | 726212 | 1469083725_5273809641 | 38328628012 + 631202 + 3262 + 582 |
10 | 977792 | 1482370659_9560732841 | 38501566982 + 201612 + 462 + 402 |
11 | 555812 | 1657429803_3089247561 | 40711543852 + 811442 + 3582 + 2062 |
12 | 839192 | 1658932407_7042398561 | 40729993952 + 732942 + 1102 + 104 |
13 | 687812 | 1695280374_4730825961 | 41173782612 + 239842 + 4502 + 782 + 103 |
14 | 757592 | 1806249375_5739426081 | 42499992652 + 569102 + 2662 + 2002 + 303 |
15 | 988022 | 4025381679_9761835204 | 63445895682 + 1157002 + 9542 + 922 |
16 | 901982 | 4029765318_8135679204 | 63480432562 + 899362 + 3362 + 262 |
17 | 912482 | 4057916238_8326197504 | 63701775782 + 1143302 + 7482 + 703 + 24 |
18 | 439022 | 4065837291_1927385604 | 63763918412 + 442252 + 4072 + 72 |
19 | 967022 | 4086721539_9351276804 | 63927470932 + 655052 + 5112 + 204 + 32 |
20 | 846482 | 4093825617_7165283904 | 63983010382 + 655222 + 4262 + 3002 + 502 |
21 | 488522 | 4097156832_2386517904 | 64009037102 + 1330182 + 9822 + 342 |
22 | 565322 | 4207685913_3195867024 | 64866677982 + 1076322 + 7862 + 703 + 3002 |
23 | 761822 | 4217963085_5803697124 | 64945847322 + 1211442 + 5402 + 1582 |
24 | 549182 | 4276895103_3015986724 | 65397974762 + 769402 + 4922 + 104 + 222 |
25 | 780722 | 4817325906_6095237184 | 69406958632 + 585652 + 2492 + 332 + 102 |
26 | 812222 | 4823107956_6597013284 | 69448599382 + 903262 + 8582 + 105 + 303 |
27 | 351722 | 4859607321_1237069584 | 69710883782 + 1932622 + 3662 + 403 + 102 |
28 | 387722 | 4897623051_1503267984 | 69983019722 + 1421402 + 5402 + 105 + 203 |
29 | 891452 | 5201386497_7946831025 | 72120638502 + 383402 + 2302 + 52 |
30 | 661052 | 5201789634_4369871025 | 72123433322 + 756612 + 6362 + 214 + 103 |
31 | 946952 | 5203417698_8967143025 | 72134719092 + 838742 + 3822 + 2122 |
32 | 980552 | 5203874169_9614783025 | 72137883042 + 684652 + 3602 + 282 |
33 | 819452 | 5203894176_6714983025 | 72138021712 + 662622 + 1242 + 422 |
34 | 893552 | 5206134897_7984316025 | 72153550832 + 648862 + 463 + 2982 |
35 | 916052 | 5206741938_8391476025 | 72157757302 + 522902 + 4452 + 103 |
36 | 584552 | 5207896143_3416987025 | 72165754642 + 762242 + 2472 + 1122 |
37 | 405452 | 5207983461_1643897025 | 72166359622 + 601012 + 3182 + 28 |
38 | 804452 | 5208931746_6471398025 | 72172929452 + 1119122 + 5702 + 662 |
39 | 379052 | 5209876341_1436789025 | 72179473122 + 1123732 + 10062 + 2462 |
40 | 615752 | 5260841973_3791480625 | 72531661862 + 1098072 + 3382 + 502 + 62 |
41 | 773462 | 6173042895_5982403716 | 78568714482 + 747282 + 7122 + 782 |
42 | 951542 | 6173824509_9054283716 | 78573688402 + 1060702 + 5802 + 3962 |
43 | 585542 | 6190758243_3428570916 | 78681371642 + 437102 + 2042 + 482 |
44 | 554462 | 6198524703_3074258916 | 78730710002 + 2490642 + 6162 + 582 |
45 | 507062 | 6348901752_2571098436 | 79679995932 + 923172 + 6632 + 403 + 36 |
46 | 427442 | 6359407281_1827049536 | 79745891922 + 1751102 + 5662 + 153 + 292 |
47 | 901442 | 6370495218_8125940736 | 79815382082 + 1495362 + 220 + 1602 |
48 | 331442 | 6374258901_1098524736 | 79838956022 + 1657182 + 7982 + 7002 + 22 |
49 | 440162 | 6528047391_1937408256 | 80796332782 + 705142 + 184 + 2302 + 302 |
50 | 609842 | 6528409173_3719048256 | 80798571602 + 878382 + 583 + 2702 + 202 |
51 | 990662 | 6532704189_9814072356 | 80825145772 + 1113392 + 4552 + 592 |
52 | 618662 | 6591047283_3827401956 | 81185265182 + 1017742 + 4662 + 1802 + 103 |
53 | 656342 | 6591287034_4307821956 | 81186741742 + 270762 + 503 + 702 + 22 |
54 | 662762 | 6718052934_4392508176 | 81963729382 + 749242 + 3882 + 23 + 22 |
55 | 456242 | 6739451802_2081549376 | 82094164222 + 1796602 + 823 + 182 |
56 | 555242 | 6754192803_3082914576 | 82183896242 + 1456422 + 4942 + 603 + 103 |
57 | 539762 | 6758043192_2913408576 | 82207318362 + 590702 + 3742 + 2702 + 22 |
58 | 556262 | 6781524903_3094251876 | 82350014582 + 1408242 + 8442 + 1202 + 202 |
59 | 371762 | 6794502831_1382054976 | 82428774282 + 1354622 + 583 + 1062 |
60 | 493142 | 6950781342_2431870596 | 83371346052 + 233072 + 3412 + 1792 |
61 | 922142 | 6971243058_8503421796 | 83493970182 + 1559342 + 8462 + 103 + 202 |
62 | 322862 | 6975832401_1042385796 | 83521448732 + 1773732 + 10072 + 672 |
63 | 393362 | 6980237451_1547320896 | 83547815342 + 1751562 + 4982 + 2302 + 502 |
64 | 784532 | 9023784516_6154873209 | 94993602502 + 829122 + 6172 + 1742 |
65 | 760472 | 9026413875_5783146209 | 95007441152 + 1306742 + 5642 + 29 + 102 |
66 | 901532 | 9043657218_8127563409 | 95098145192 + 484142 + 5662 + 503 + 64 |
67 | 594032 | 9046178253_3528716409 | 95111399172 + 1130362 + 743 + 703 + 403 |
68 | 853532 | 9064315827_7285134609 | 95206700542 + 123582 + 2272 |
69 | 358532 | 9067345821_1285437609 | 95222611922 + 511482 + 383 + 632 |
70 | 391472 | 9067842351_1532487609 | 95225219092 + 643922 + 106 + 3922 |
71 | 493532 | 9068175342_2435718609 | 95226967512 + 1045422 + 903 + 622 |
72 | 858032 | 9084512637_7362154809 | 95312709732 + 1288782 + 4142 + 2702 + 702 |
73 | 886232 | 9216304587_7854036129 | 96001586382 + 555652 + 7422 + 64 |
74 | 860732 | 9231658047_7408561329 | 96081517722 + 601792 + 5482 + 203 + 103 |
75 | 676772 | 9236710854_4580176329 | 96107808492 + 1306682 + 7982 + 5002 + 502 |
76 | 895232 | 9257634108_8014367529 | 96216599962 + 968892 + 4062 + 662 |
77 | 857432 | 9402681537_7351862049 | 96967425132 + 1180242 + 8002 + 482 |
78 | 357572 | 9403658721_1278563049 | 96972463722 + 1095962 + 3402 + 432 |
79 | 320432 | 9483576201_1026753849 | 97383654682 + 1506382 + 2102 + 2092 |
80 | 687632 | 9610538274_4728350169 | 98033352862 + 1224552 + 6482 + 382 |
81 | 695132 | 9617502384_4832057169 | 98068865522 + 321472 + 4162 + 702 + 302 |
82 | 353372 | 9653078421_1248703569 | 98250081022 + 829642 + 1872 + 302 |
83 | 465872 | 9658430712_2170348569 | 98277315342 + 1333862 + 7242 + 792 |
84 | 584132 | 9658702143_3412078569 | 98278696282 + 919072 + 5562 + 1202 |
85 | 656372 | 9675128034_4308215769 | 98362228692 + 1251762 + 6962 + 105 + 962 |
86 | 455672 | 9841536702_2076351489 | 99204519562 + 1037882 + 3402 + 2472 |
87 | 714332 | 9843762015_5102673489 | 99215734712 + 1210422 + 5282 + 4902 + 103 |
|
E. Reverse Elevendigital Cubes as Sum of Powers | |||||
---|---|---|---|---|---|
Sl.No | Power | Elevendigit cube |
| Sum Of Powers | |
1 | 25353 | 16290480375 | 57308409261 | 2393912 + 5742 + 1702 + 22 | |
2 | 27953 | 21834609875 | 57890643812 | 2406042 + 5642 + 2002 + 302 | |
3 | 35063 | 43095878216 | 61287859034 | 2475622 + 8732 + 3902 + 312 | |
4 | 23263 | 12584301976 | 67910348521 | 2605952 + 6002 + 4802 + 212 | |
5 | 31233 | 30459021867 | 76812095403 | 2771472 + 12762 + 872 + 72 | |
6 | 39093 | 59730618429 | 92481603795 | 3041072 + 6352 + 503 + 203 + 112 |
|
F. Palindromic Twin Elevendigitals as Sum of Powers | |||
---|---|---|---|
Sl.No | Power | Palindrome - 22 digits | Sum Of Powers |
Elevendigit cube_Reversed cube | |||
1 | 23263 | 12584301976_67910348521 | 354743597212 + 2302242 + 343 + 1402 + 402 |
2 | 25353 | 16290480375_57308409261 | 403614672372 + 1840762 + 1462 |
3 | 27953 | 21834609875_57890643812 | 467275185252 + 2316732 + 2872 + 832 |
4 | 31233 | 30459021867_76812095403 | 551896927582 + 2331832 + 3692 + 332 + 102 |
5 | 35063 | 43095878216_61287859034 | 656474509912 + 2134012 + 9952 + 102 + 33 |
6 | 39093 | 59730618429_92481603795 | 772855862562 + 2426212 + 7272 + 303 + 332 |
Sl.No | Power | Reversed cube_Elevendigit cube | Sum Of Powers |
1 | 25353 | 57308409261_16290480375 | 757023178382 + 2659252 + 11202 + 3552 + 34 |
2 | 27953 | 57890643812_21834609875 | 760859013302 + 1527702 + 553 + 402 + 102 |
3 | 35063 | 61287859034_43095878216 | 782865627252 + 3843642 + 155 + 922 + 28 |
4 | 23263 | 67910348521_12584301976 | 824077353902 + 657702 + 3962 + 122 + 24 |
5 | 31233 | 76812095403_30459021867 | 876425098922 + 4014232 + 7652 + 204 + 72 |
6 | 39093 | 92481603795_59730618429 | 961673561012 + 3212282 + 8402 + 7502 + 122 |
|
G. Palindromic 32_digitals as Sum of Powers | ||||
---|---|---|---|---|
Sl.No | Power | Palindrome - 32 digits | Sum Of Powers | |
Reversed cube_Repdigital_Elevendigit cube | ||||
1 | 25353 | 57308409261_9999999999_16290480375 | 75702317839019962 + 577531372 + 111462 + 3452 + 572 | |
2 | 27953 | 57890643812_7777777777_21834609875 | 76085901330521002 + 706884752 + 47302 + 352 + 53 | |
3 | 35063 | 61287859034_3333333333_43095878216 | 78286562725881212 + 322227772 + 52802 + 57 + 1392 | |
5 | 23263 | 67910348521_9999999999_12584301976 | 82407735390556632 + 558919192 + 127422 + 2512 + 912 | |
4 | 31233 | 76812095403_5555555555_30459021867 | 87642509893062482 + 2061483 + 836812 + 8072 + 3312 | |
6 | 39093 | 92481603795_1111111111_59730618429 | 96167356101283712 + 1381200942 + 162722 + 217 + 1642 |
|
H. Palindromic 63_digitals as Sum of Powers | ||||
---|---|---|---|---|
Mid No. | Palindrome - 63 digits | |||
Sum Of Powers | ||||
ZERO | 3433683820_29251248465_7849089281_Z_1829809487_5648421529_20283863343 9032 + 13527045085918952 + 449337802 + 62502 + 1132 + 932 | |||
1 | 3433683820_29251248465_7849089281_1_1829809487_5648421529_20283863343 9032 + 34394490092985592 + 562003122 + 39342 + 1112 + 292 | |||
2 | 3433683820_29251248465_7849089281_2_1829809487_5648421529_20283863343 9032 + 46722381668280612 + 466934932 + 76272 + 3622 + 202 | |||
3 | 3433683820_29251248465_7849089281_3_1829809487_5648421529_20283863343 9032 + 56417913367621842 + 1052666312 + 104542 + 1912 + 36 | |||
5 | 3433683820_29251248465_7849089281_4_1829809487_5648421529_20283863343 9032 + 64675968866005272 + 1097553722 + 111462 + 2952 + 832 | |||
4 | 3433683820_29251248465_7849089281_5_1829809487_5648421529_20283863343 9032 + 71992922907439202 + 548781672 + 3773 + 1852 + 142 | |||
6 | 3433683820_29251248465_7849089281_6_1829809487_5648421529_20283863343 9032 + 78631933390680942 + 256410582 + 77272 + 672 + 53 | |||
7 | 3433683820_29251248465_7849089281_7_1829809487_5648421529_20283863343 9032 + 84752468688271752 + 898452012 + 110692 + 3502 + 842 | |||
8 | 3433683820_29251248465_7849089281_8_1829809487_5648421529_20283863343 9032 + 90459830581073302 + 81042252 + 46042 + 174 + 592 | |||
9 | 3433683820_29251248465_7849089281_9_1829809487_5648421529_20283863343 = {Sum Of Powers} ? Power columns against the last 63 digital palindrome are left blank, inviting enthusiastic readers to compute appropriate powers. There can be several such choices ! It is an intellectual and educating exercise to weave the last few powers. I remember to have laid a well designed trap to get a square and cube totalling 8055299079 Vide WON 178. |
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A000179 Prime Curios! Prime Puzzle Wikipedia 179 Le nombre 179 |
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