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

11, 101, 151, 1598951, 1128512158211, 104216919612401, 107635959536701, 106906347292743609601, 165901968762984246868642489267869109561

Offset

1,1

Comments

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.

a(9) > 10^25. - Donovan Johnson, Feb 13 2011

a(10) > 10^39. - 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[ f ] ], {k, 1, 500000} ]

Crossrefs

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.

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

Sequence in context: A052035 A083144 A058411 * A156753 A118592 A156617

Adjacent sequences: A134459 A134460 A134461 * A134463 A134464 A134465

Keyword

more,nonn,base

Author

Alexander Adamchuk, Oct 26 2007

Extensions

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

a(8) from Donovan Johnson, Feb 13 2011

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

Status

approved