A178033 Lesser of a twin prime pair (p,p+2) such that permuting the digits of p and those of p+2 gives a different twin prime pair (q, q+2).

281, 461, 641, 821, 1031, 1091, 1229, 1277, 1301, 1319, 1427, 1697, 1721, 1787, 1877, 2081, 2129, 2381, 2687, 2711, 2801, 3119, 3251, 3257, 3371, 3467, 3527, 3581, 3821, 3851, 4091, 4127, 4157, 4217, 4241, 4271, 4421, 4517, 4637, 4649, 4721, 4787, 4931, 4967, 5231, 5417, 5477, 5651

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 17 2010

Keywords

• nonn
• base

Comments

Permutations with initial zeros are disallowed, so that 101 is not a member (101,103 and 11,13); equivalently, we require that p is a permutation of the digits of q as well.

Examples

			281 is a term as 281 is the lesser of the twin prime pair 281,283, and after permuting 821, 823 is also a twin prime pair.
1229 is a term as (1229,1231) is a twin prime pair and after permuting (2129, 2131) is also a twin prime pair.
		

Links

• Hans Rudolf Widmer, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001359, A172271, A172494, A173255, A174454

Programs

Mathematica

perm@n_ :=
 Select[FromDigits@# & /@
   DeleteCases[Rest@Permutations@IntegerDigits@n, _?(First@# == 0 &)],
   PrimeQ];
Cases[{#, perm@# & /@ #} & /@
  Cases[6*# + {-1, 1} & /@
    Range@2000, {?PrimeQ ..}], {{x, }, {{__, a_, _}, {_, b_, _}} /; b - a == 2} :> x] (* Hans Rudolf Widmer, Oct 04 2024 *)

Extensions

Corrected and edited by D. S. McNeil, Nov 23 2010

More terms from Hans Rudolf Widmer, Oct 04 2024