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

13, 17, 37, 79, 107, 113, 127, 131, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 197, 199, 239, 241, 251, 277, 281, 283, 313, 337, 347, 349, 359, 367, 373, 379, 389, 397, 419, 457, 461, 463, 467, 479, 491, 563, 569, 571, 577, 587, 593, 613

Offset: 1

Author

Pierre CAMI, Oct 18 2009

Keywords

• nonn
• base

Comments

Primes like 113, 137, 149, 157 etc have more than one such larger anagram, but are only listed once.

Examples

			13 is the first with 31 as prime anagram.
17 is the second with 71 as prime anagram.
31 has one anagram 13 but this is not >31 so 31 is not in the sequence.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055387, A109308, A069567.

Programs

Maple

filter:= proc(p) local L,Lp,q,i;
  if not isprime(p) then return false fi;
  L:= convert(p,base,10);
  for Lp in combinat:-permute(L) do
    q:= add(Lp[i]*10^(i-1),i=1..nops(L));
    if q > p and isprime(q) then return true fi
  od;
false
end proc:
select(filter, [seq(i,i=13..1000,2)]); # Robert Israel, Jan 18 2023

Mathematica

paQ[n_]:=Length[Select[FromDigits/@Permutations[IntegerDigits[n]],#>n && PrimeQ[#]&]]>0; Select[Prime[Range[200]],paQ] (* Harvey P. Dale, Sep 23 2013 *)

Python

from itertools import islice
from sympy.utilities.iterables import multiset_permutations
from sympy import isprime, nextprime
def A166681_gen(): # generator of terms
    p = 13
    while True:
        for q in multiset_permutations(str(p)):
            if (r:=int(''.join(q)))>p and isprime(r):
                yield p
                break
        p = nextprime(p)
A166681_list = list(islice(A166681_gen(),20)) # Chai Wah Wu, Jan 17 2023

Extensions

Definition clarified, sequence extended. - R. J. Mathar, Oct 12 2012