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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A055387, A109308, A069567.

Sequence in context: A174056 A307894 A322472 * A109308 A263241 A246944

Adjacent sequences: A166678 A166679 A166680 * A166682 A166683 A166684

Keyword

nonn,base

Author

Pierre CAMI, Oct 18 2009

Extensions

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

Status

approved