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A359137 Primes such that there is a nontrivial permutation which when applied to the digits produces a prime (Version 2).

%I A359137 #27 Jan 23 2023 12:07:20
%S A359137 11,13,17,31,37,71,73,79,97,101,107,113,127,131,137,139,149,151,157,
%T A359137 163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,
%U A359137 271,277,281,283,293,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,419,421
%N A359137 Primes such that there is a nontrivial permutation which when applied to the digits produces a prime (Version 2).
%C A359137 A prime p with decimal expansion p = d_1 d_2 ... d_m is in this sequence iff there is a non-identity permutation pi in S_m such that q = d_pi(1) d_pi(2) ... d_pi(m) is also a prime. The prime q may or may not be equal to p. Leading zeros are not permitted in q.
%C A359137 One must be careful when using the phrase "nontrivial permutation of the digits". When the first and third digits of 101 are exchanged, this is applying the nontrivial permutation (1,3) in S_3 to the digits, leaving the number itself unchanged. One should specify whether it is the permutation that is nontrivial, or its action on what is being permuted. In this sequence and A359136, we mean that the permutation itself is nontrivial.
%C A359137 There are only 53 primes not in this sequence, the greatest of which is 8059. - _Andrew Howroyd_, Jan 22 2023
%H A359137 Andrew Howroyd, <a href="/A359137/b359137.txt">Table of n, a(n) for n = 1..1000</a>
%o A359137 (PARI) isok(n)={my(v=vecsort(digits(n))); if(#Set(v)<#v, 1, forperm(v, u, if(u[1]<>0, my(t=fromdigits(Vec(u))); if(isprime(t) && t<>n, return(1)))); 0)} \\ _Andrew Howroyd_, Jan 22 2023
%o A359137 (Python)
%o A359137 from sympy import isprime
%o A359137 from itertools import permutations as P
%o A359137 def ok(n):
%o A359137     if not isprime(n): return False
%o A359137     if len(s:=str(n)) > len(set(s)): return True
%o A359137     return any(isprime(t) for t in (int("".join(p)) for p in P(s) if p[0]!="0") if t!=n)
%o A359137 print([k for k in range(422) if ok(k)]) # _Michael S. Branicky_, Jan 23 2023
%Y A359137 Cf. A359136, A359138, A359139.
%K A359137 nonn,base
%O A359137 1,1
%A A359137 _N. J. A. Sloane_ and _Allan C. Wechsler_, Jan 22 2023
%E A359137 More than the usual number of terms are shown in order to distinguish this from other similar sequences.
%E A359137 Incorrect terms removed by _Andrew Howroyd_, Jan 22 2023