WON TOPIC 227

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[ October 9, 2023 ] [ Last update November 14, 2023 ] Bringing palindrome 10901 into an interesting state. By Patrick De Geest This WONplate will bring the palindrome 10901 to the foreground by highlighting as much properties as possible. Let me start with these four curiosa. Readers are encouraged to send in more oddities, peculiarities, whimsicalties or whatever particularity they can muster. ( symbol ^^ stands for concatenation ) 10901 = 5⁵ + 6⁵ Source → WONplate 145 → A003347 → A074615 → A217845 → A226814 → A247099 → A250546 → A228542 The smallest palindromic prime of length 37 is formed with the use of 10901 [1]^^[0]₁₅^^[10901]^^[0]₁₅^^[1] Source → Palprime Page 1 You need to append 33 nines to 10901 to get a first prime. [10901][9^^33] Source → Appending 9s to k.txt Multiplying palindrome 10901 with palindrome 11 results in a third palindrome 10901 * 11 = 119911 Source → A229805 Multiplying palindrome 10901 with palindrome 1001 results in a third palindrome 10901 * 1001 = 10911901 Source → Ninedigits Page 7 Alexandru Petrescu [ November 1, 2023 ] delved into the Fibonacci numbers and found 16 non consecutive terms that sums up to 10901. 1, 1, ₂, 3, 5, ₈, 13, 21, ₃₄, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, ₆₇₆₅, ₁₀₉₄₆, ... they are marked in darkbrown color. PDG inspired by Alexandru found an expression with only 4 Fibonacci terms 10901 = 10946 – 55 + 5 + 5 Alexandru Petrescu [ November 1, 2023 ] There are 23 palprimes less than 10901, namely 2,3,5,7,11,101,131,151,181,191,313,353,373, 383,727,787,797,919,929,10301,10501 and 10601 Alexandru tried to express 10901 as a sum of different palprimes from this list. Due to the large gap between 929 and 10301 it's obvious that one of a term might be 10301, 10501 or 10601. He obtained a number of such representations having 5, 6, 7, 8 or 9 terms. Exemplification: 10901 = 3 + 5 + 101 + 191 + 10601 (5 terms) 10901 = 3 + 5 + 7 + 11 + 101 + 131 + 151 + 191 + 10301 (9 terms) Alexandru Petrescu [ November 13, 2023 ] 10901is a semiprime → 11 * 991 with the following very nice notability 10901 is the sum of 11 consecutive primes, 991 being the median of this sequence. In formal notation → prime(162) + prime(163) + ... + prime(171) + prime(172) or written out 10901 = 953 + 967 + 971 + 977 + 983 + 991 + 997 + 1009 + 1013 + 1019 + 1021 YOUR TURN with 10901
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[ October 9, 2023 ] [ Last update November 14, 2023 ]
Bringing palindrome 10901 into an interesting state.
By Patrick De Geest

This WONplate will bring the palindrome 10901 to the foreground
by highlighting as much properties as possible.
Let me start with these four curiosa. Readers are
encouraged to send in more oddities, peculiarities,
whimsicalties or whatever particularity they can muster.
( symbol ^^ stands for concatenation )

10901 = 5⁵ + 6⁵
Source → WONplate 145
→ A003347 → A074615 → A217845
→ A226814 → A247099 → A250546
→ A228542

The smallest palindromic prime of length 37
is formed with the use of 10901
[1]^^[0]₁₅^^[10901]^^[0]₁₅^^[1]
Source → Palprime Page 1

You need to append 33 nines to 10901 to get a first prime.
[10901][9^^33]
Source → Appending 9s to k.txt

Multiplying palindrome 10901 with palindrome 11 results in a third palindrome
10901 * 11 = 119911
Source → A229805
Multiplying palindrome 10901 with palindrome 1001 results in a third palindrome
10901 * 1001 = 10911901
Source → Ninedigits Page 7

Alexandru Petrescu [ November 1, 2023 ]

delved into the Fibonacci numbers and found 16
non consecutive terms that sums up to 10901.
1, 1, ₂, 3, 5, ₈, 13, 21, ₃₄, 55, 89, 144, 233,
377, 610, 987, 1597, 2584, 4181, ₆₇₆₅, ₁₀₉₄₆, ...
they are marked in darkbrown color.

PDG inspired by Alexandru found an expression with only 4 Fibonacci terms
10901 = 10946 – 55 + 5 + 5

Alexandru Petrescu [ November 1, 2023 ]

There are 23 palprimes less than 10901, namely
2,3,5,7,11,101,131,151,181,191,313,353,373,
383,727,787,797,919,929,10301,10501 and 10601
Alexandru tried to express 10901 as a sum of different palprimes from this list.
Due to the large gap between 929 and 10301 it's obvious that one of a term
might be 10301, 10501 or 10601.
He obtained a number of such representations having 5, 6, 7, 8 or 9 terms. Exemplification:
10901 = 3 + 5 + 101 + 191 + 10601 (5 terms)
10901 = 3 + 5 + 7 + 11 + 101 + 131 + 151 + 191 + 10301 (9 terms)

Alexandru Petrescu [ November 13, 2023 ]

10901is a semiprime → 11 * 991
with the following very nice notability
10901 is the sum of 11 consecutive primes, 991 being
the median of this sequence.
In formal notation → prime(162) + prime(163) + ... + prime(171) + prime(172)
or written out
10901 = 953 + 967 + 971 + 977 + 983 + 991 + 997 + 1009 + 1013 + 1019 + 1021

YOUR TURN with 10901

A000227

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Patrick De Geest - Belgium

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E-mail address : pdg@worldofnumbers.com