A032594 Greater of two consecutive palindromes, both of which are prime.

3, 191, 383, 797, 929, 10601, 11411, 12821, 13931, 15551, 16661, 19991, 30203, 30803, 32423, 35153, 38183, 70607, 77477, 78887, 93239, 94949, 1093901, 1178711, 1243421, 1281821, 1287821, 1328231, 1363631, 1412141, 1464641, 1490941, 1551551

Offset

1,1

Comments

Original name: Twin palindromic primes (upper terms).

Twin palindromic primes are of odd length and differ by one from the middle digit outwards. There are no palindromic primes of even length except 11.

Conjecture: sequence is finite. - Charles R Greathouse IV, Mar 22 2011

References

Martin Gardner, "The Ambidextrous Universe", Penguin Press, Sec. Ed. 1982, pp. 39-41.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Patrick De Geest, World!Of Palindromic Primes

Sean A. Irvine, Java program (github)

Mathematica

nLP[cn_Integer]:=Module[{s, len, half, left, pal, fdpal}, s=IntegerDigits[cn]; len=Length[s]; half=Ceiling[len/2]; left=Take[s, half]; pal=Join[left, Reverse[Take[left, Floor[len/2]]]]; fdpal=FromDigits[pal]; Which[cn==9, 11, fdpal>cn, fdpal, True, left=IntegerDigits[FromDigits[left]+1]; pal=Join[left, Reverse[Take[left, Floor[len/2]]]]; FromDigits[pal]]]; Select[Partition[NestList[nLP, 1, 3000], 2, 1], AllTrue[#, PrimeQ]&][[;; , 2]] (* Harvey P. Dale, Sep 07 2025 *)

Crossrefs

Cf. A002385 (palindromic primes), A032593 (lesser terms).

Sequence in context: A158469 A261000 A365447 * A159658 A257038 A202109

Adjacent sequences: A032591 A032592 A032593 * A032595 A032596 A032597

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Extensions

Changed offset to 1 by N. J. A. Sloane, Feb 15 2015

Name changed by Sean A. Irvine, Sep 06 2025

Status

approved