World!OfNumbers |
WON plate 152 | |
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The scientific name is commonly used in zoölogy for naming species Transferred to the world of numbers the analogy brings us to No better introduction to tautonymic numbers than pointing your attention This wonplate will collect tautonymic numbers that show
Allow me to start with the number of the song title 2525 itself. 2525 = (9–2) 6565 = (2–5)
9595 when raised to the fourth power is a number
^{2}^{2}Enjoy the following neat fact that
A triangular tautonymic number
The string formed by concatenating
A Kaprekar tautonymic number
9696 * 2
The decimal expansion of 499
From the Prime Curios! database :
The smallest (probable) prime of 35631 digits is situated at
Are you creative and adventurous enough to discover
" Here is an old idea that may be worth considering. The magician says : "Choose any 3-place number you wish and write it down." Let's say, by way of example, the patsy choose 276. Now the magician says : "Form a 6-place number by writing it beside itself." For our example, this means 276276. A tautonym has been produced. Magician : "Divide that result by 7." Result is 39468. Magician : "Divide that result by 11." Result is 3588. Magician : "Divide that result by 13, and report what you have." Of course, the patsy now has the original number, 276, once again !
Here is something that emerged while I was investigating P = 5882353 = 588 Now multiply this famous prime with another famous prime '13' Moreover N = 76470589 when split into two halves and ps. 7647 + 2353 = 10000 exactly ps. note also this infinite beast pattern and the next one was spotted by Jean Claude Rosa Tautonymic numbers of the form (N) * (N+1) 1. 132_132 = 363 * 364 JCR noticed also this nice '0 640319720239800_640319720239800 = 64003199720023998000_64003199720023998000 = 6400031999720002399980000_6400031999720002399980000 = etc. The method used by JCR : T_T = T*(10^L+1) where L = number of digits of T. JCR found all solutions of T_T = N*(N+1) up to 38 digits for T_T. Here is an explanation why N or N+1 cannot be prime :
We have : T_T = T*(10^L+1) = N*(N+1) Continuation of the table (smallest-largest only) : T_T with 24 digits : 5 solutions T_T with 26 digits : 4 solutions T_T with 28 digits : 11 solutions T_T with 30 digits : 91 solutions T_T with 32 digits : 17 solutions T_T with 34 digits : 11 solutions T_T with 36 digits : 5 solutions T_T with 38 digits : 2 solutions
Thus far JCR only discovered one solution namely :
1. 78 * 79 = 61_62 781340266 * 781340265 = 610492_610491_610490 19 * 20 * 21 = 79_80 13 * 12 * 11 = 17_16 Can you find larger/other examples ?
1. 183_184 = 428 (4 Among the first 33333 values of n [PDG, The squareroot is an intertwining of Palindrome 909090909 (with nine digits btw!) squared (1 727 + 274 = 1001 a palindrome 727 x 274 = 199_198 a tautonym of the form (T)_(T – 1)
Jean-Claude Rosa found many new patterns : 3(9 Fascinating 9090909090911 Two more patterns which, JCR hopes, might give better results : P=(54 P=(72
1. 82_81 = 91 discover with JCR this 'joli' pattern (see nrs. 1, 3, 5, 7, 11 & 16) (9 326666333267 + 673333666734 = 1000000000001 their palindromic sum ! 326666333267 * 673333666734 = 219955439977_219955439978 their product a near_tautonymic number of the form (T)_(T+1) !
The first pattern I investigated is (9 Regarding p^2 = T_(T-1) here is a pattern (again by JCR!)
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A000152 Prime Curios! Prime Puzzle Wikipedia 152 Le nombre 152 |

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