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

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

Offset

1,2

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

Table of n, a(n) for n=1..9.

Patrick De Geest, Palindromic Centered Polygonal Numbers

Eric Weisstein's World of Mathematics, Palindromic Prime

Wikipedia, Centered decagonal number

Mathematica

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

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.

Sequence in context: A368531 A042717 A304286 * A298938 A309071 A270975

Adjacent sequences: A134460 A134461 A134462 * A134464 A134465 A134466

Keyword

more,nonn,base

Author

Alexander Adamchuk, Oct 26 2007

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

Status

approved