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

1, 4, 5, 565, 475081, 4565455, 4639740, 4623988479, 5760242508141202328

Offset: 1

Author

Alexander Adamchuk, Oct 26 2007

Keywords

• more
• nonn
• base

Comments

Corresponding centered decagonal palindromic primes are 5k^2 + 5k + 1 = A134462 = {11, 101, 151, 1598951, 1128512158211, ...}. Note that the first 4 terms of A134463 are palindromic as well.

a(9) > 1414213562372. - Donovan Johnson, Feb 13 2011

a(10) > 14142135623730950488. - Patrick De Geest, May 29 2021

Links

• Patrick De Geest, Palindromic Centered Polygonal Numbers
• Eric Weisstein's World of Mathematics, Palindromic Prime
• Wikipedia, Centered decagonal number

Crossrefs

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

Cf. A002385 = Palindromic primes.

Cf. A062786 = Centered 10-gonal numbers.

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

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

Programs

Mathematica

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

Extensions

a(6), a(7) from D. S. McNeil, Mar 02 2009

a(8) from Donovan Johnson, Feb 13 2011

a(9) from Patrick De Geest, May 29 2021