A180541 Primes that become a different prime under the mapping 3 <=> 5.

3, 5, 131, 137, 151, 157, 337, 347, 547, 557, 839, 859, 1031, 1051, 1367, 1439, 1459, 1567, 1637, 1657, 1931, 1951, 2351, 2531, 2837, 2857, 3011, 3119, 3167, 3209, 3251, 3257, 3301, 3307, 3319, 3391, 3407, 3449, 3457, 3547, 3581, 3631, 3637, 3659, 3701

Offset: 1

Author

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index to Primes, Primes that become a different prime under some mapping.

Crossrefs

Cf. A171026, A175791, A180517 thru A180559, A175789, A180560, A180561.

Programs

Maple

filter:= proc(n) local L,Lp,i,x;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  Lp:= subs([3=5,5=3],L);
  if L=Lp then return false fi;
  isprime(add(Lp[i]*10^(i-1),i=1..nops(Lp)))
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Jul 28 2020

Mathematica

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 3] || MemberQ[id, 5]) && PrimeQ[ FromDigits[ id /. {3 -> 5, 5 -> 3}] ]]; Select[ Prime@ Range@ 550, fQ]