cp's OEIS Frontend

A318295 Prime numbers whose digits can be permuted in multiple ways to yield primes.

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