A134462 - OEIS

%I #22 Jun 02 2021 22:31:33

%S 11,101,151,1598951,1128512158211,104216919612401,107635959536701,

%T 106906347292743609601,165901968762984246868642489267869109561

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

%C 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 a(9) > 10^25. - _Donovan Johnson_, Feb 13 2011

%C a(10) > 10^39. - _Patrick De Geest_, May 29 2021

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/centered.htm">Palindromic Centered Polygonal Numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicPrime.html">Palindromic Prime</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Centered_decagonal_number">Centered decagonal number</a>.

%t Do[ f=5k^2+5k+1; If[ PrimeQ[f] && FromDigits[ Reverse[ IntegerDigits[ f ] ] ] == f, Print[ f ] ], {k, 1, 500000} ]

%Y Cf. A002385 = Palindromic primes.

%Y Cf. A062786 = Centered 10-gonal numbers.

%Y Cf. A090562 = Primes of the form 5k^2 + 5k + 1.

%Y Cf. A090563 = Values of k such that 5k^2 + 5k + 1 is a prime.

%Y Cf. A134463 = Values of k such that 5k^2 + 5k + 1 is a palindromic prime.

%K more,nonn,base

%O 1,1

%A _Alexander Adamchuk_, Oct 26 2007

%E More terms from Tomas J. Bulka (tbulka(AT)rodincoil.com), Aug 30 2009

%E a(8) from _Donovan Johnson_, Feb 13 2011

%E a(9) from _Patrick De Geest_, May 29 2021