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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).
1
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
1,1
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.
LINKS
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 17 2010
EXTENSIONS
Corrected and edited by D. S. McNeil, Nov 23 2010
More terms from Hans Rudolf Widmer, Oct 04 2024
STATUS
approved