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A166681 Primes p which have at least one prime anagram larger than p.

%I A166681 #21 Jan 18 2023 15:58:05
%S A166681 13,17,37,79,107,113,127,131,137,139,149,157,163,167,173,179,181,191,
%T A166681 197,199,239,241,251,277,281,283,313,337,347,349,359,367,373,379,389,
%U A166681 397,419,457,461,463,467,479,491,563,569,571,577,587,593,613
%N A166681 Primes p which have at least one prime anagram larger than p.
%C A166681 Primes like 113, 137, 149, 157 etc have more than one such larger anagram, but are only listed once.
%H A166681 R. J. Mathar, <a href="/A166681/b166681.txt">Table of n, a(n) for n = 1..1000</a>
%e A166681 13 is the first with 31 as prime anagram.
%e A166681 17 is the second with 71 as prime anagram.
%e A166681 31 has one anagram 13 but this is not >31 so 31 is not in the sequence.
%p A166681 filter:= proc(p) local L,Lp,q,i;
%p A166681   if not isprime(p) then return false fi;
%p A166681   L:= convert(p,base,10);
%p A166681   for Lp in combinat:-permute(L) do
%p A166681     q:= add(Lp[i]*10^(i-1),i=1..nops(L));
%p A166681     if q > p and isprime(q) then return true fi
%p A166681   od;
%p A166681 false
%p A166681 end proc:
%p A166681 select(filter, [seq(i,i=13..1000,2)]); # _Robert Israel_, Jan 18 2023
%t A166681 paQ[n_]:=Length[Select[FromDigits/@Permutations[IntegerDigits[n]],#>n && PrimeQ[#]&]]>0; Select[Prime[Range[200]],paQ] (* _Harvey P. Dale_, Sep 23 2013 *)
%o A166681 (Python)
%o A166681 from itertools import islice
%o A166681 from sympy.utilities.iterables import multiset_permutations
%o A166681 from sympy import isprime, nextprime
%o A166681 def A166681_gen(): # generator of terms
%o A166681     p = 13
%o A166681     while True:
%o A166681         for q in multiset_permutations(str(p)):
%o A166681             if (r:=int(''.join(q)))>p and isprime(r):
%o A166681                 yield p
%o A166681                 break
%o A166681         p = nextprime(p)
%o A166681 A166681_list = list(islice(A166681_gen(),20)) # _Chai Wah Wu_, Jan 17 2023
%Y A166681 Cf. A055387, A109308, A069567.
%K A166681 nonn,base
%O A166681 1,1
%A A166681 _Pierre CAMI_, Oct 18 2009
%E A166681 Definition clarified, sequence extended. - _R. J. Mathar_, Oct 12 2012