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