%I #31 Sep 25 2024 18:03:25
%S 103,107,113,131,137,149,157,163,167,173,179,197,199,307,311,317,337,
%T 359,373,379,389,397,419,491,571,593,613,617,631,701,709,719,733,739,
%U 751,761,839,907,919,937,941,953,971,983,991,1009,1013,1019,1021,1031,1033
%N Prime numbers whose digits can be permuted in multiple ways to yield primes.
%C From _Robert Israel_, Sep 06 2018: (Start)
%C "Multiple ways" here means more than one nontrivial permutation other than the identity permutation, i.e., there are at least 3 different primes formed by permuting digits of this prime.
%C Leading 0's are allowed in the permutations. (End)
%H Robert Israel, <a href="/A318295/b318295.txt">Table of n, a(n) for n = 1..10000</a>
%e 131 belongs to this sequence as there are two nontrivial permutations of its digits which yield other primes, namely 113 and 311.
%e 137 also belongs to this sequence. Even though 371, 713 and 731 are composite, 173 and 317 are prime, satisfying the requirement.
%e 139 does not belong in this sequence. Although 193 is prime, 319, 391, 913 and 931 are all composite.
%p filter:= proc(n) local L,Lp,t,i,m,x;
%p if not isprime(n) then return false fi;
%p L:= convert(n,base,10);
%p m:= nops(L);
%p Lp:= combinat:-permute(L);
%p t:= 1;
%p for i from 1 to nops(Lp) do
%p if Lp[i]=L then next fi;
%p x:= add(Lp[i][j]*10^(j-1),j=1..m);
%p if isprime(x) then
%p t:= t+1;
%p if t = 3 then return true fi;
%p fi
%p od;
%p false
%p end proc:
%p select(filter, [seq(i,i=11..2000,2)]); # _Robert Israel_, Sep 06 2018
%t Select[Prime[Range[200]], Count[PrimeQ[Map[FromDigits, Permutations[IntegerDigits[#]]]], True] > 2 &] (* _Alonso del Arte_, Aug 24 2018 *)
%t Select[Prime[Range[200]],Count[FromDigits/@Rest[Permutations[IntegerDigits[#]]],_?PrimeQ]>1&] (* _Harvey P. Dale_, Sep 25 2024 *)
%o (Python)
%o from itertools import *
%o nmax=1000
%o def is_prime(num):
%o if num == 0 or num == 1: return(0)
%o for k in range(2, num):
%o if (num % k) == 0:
%o return(0)
%o return(1)
%o ris = ""
%o for i in range(nmax):
%o f=0
%o lf=[]
%o if is_prime(i):
%o for p in permutations(str(i), len(str(i))):
%o k=int(''.join(p))
%o if k!=i and is_prime(k):
%o if k not in lf:
%o f+=1
%o lf.append(k)
%o if f>1:
%o ris = ris+str(i)+","
%o break
%o print(ris)
%Y Subsequence of A055387.
%K nonn,base
%O 1,1
%A _Pierandrea Formusa_, Aug 23 2018
%E More terms from _Giovanni Resta_, Sep 03 2018