cp's OEIS Frontend

A134462 Centered decagonal palindromic primes; or palindromic primes of the form 5k^2 + 5k + 1.

%I A134462 #23 Feb 16 2025 08:33:07
%S A134462 11,101,151,1598951,1128512158211,104216919612401,107635959536701,
%T A134462 106906347292743609601,165901968762984246868642489267869109561
%N A134462 Centered decagonal palindromic primes; or palindromic primes of the form 5k^2 + 5k + 1.
%C A134462 Sequence is the intersection of the palindromic primes = A002385 = {2, 3, 5, 7, 11, 101, 131, 151, ...} and the centered 10-gonal numbers = A062786 = {1, 11, 31, 61, 101, 151, ...}. Corresponding numbers k such that 5k^2 + 5k + 1 is a term of A134462 are listed in A134463 = {1, 4, 5, 565, 475081, ...}. Note that the first 4 terms of A134463 are palindromic as well.
%C A134462 a(9) > 10^25. - _Donovan Johnson_, Feb 13 2011
%C A134462 a(10) > 10^39. - _Patrick De Geest_, May 29 2021
%H A134462 Patrick De Geest, <a href="http://www.worldofnumbers.com/centered.htm">Palindromic Centered Polygonal Numbers</a>
%H A134462 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicPrime.html">Palindromic Prime</a>
%H A134462 Wikipedia, <a href="http://en.wikipedia.org/wiki/Centered_decagonal_number">Centered decagonal number</a>.
%t A134462 Do[ f=5k^2+5k+1; If[ PrimeQ[f] && FromDigits[ Reverse[ IntegerDigits[ f ] ] ] == f, Print[ f ] ], {k, 1, 500000} ]
%Y A134462 Cf. A002385 = Palindromic primes.
%Y A134462 Cf. A062786 = Centered 10-gonal numbers.
%Y A134462 Cf. A090562 = Primes of the form 5k^2 + 5k + 1.
%Y A134462 Cf. A090563 = Values of k such that 5k^2 + 5k + 1 is a prime.
%Y A134462 Cf. A134463 = Values of k such that 5k^2 + 5k + 1 is a palindromic prime.
%K A134462 more,nonn,base
%O A134462 1,1
%A A134462 _Alexander Adamchuk_, Oct 26 2007
%E A134462 More terms from Tomas J. Bulka (tbulka(AT)rodincoil.com), Aug 30 2009
%E A134462 a(8) from _Donovan Johnson_, Feb 13 2011
%E A134462 a(9) from _Patrick De Geest_, May 29 2021