A175789 Primes that become another prime under the map 8 <-> 9 (acting on the decimal digits).

181, 191, 283, 293, 787, 797, 811, 853, 877, 881, 887, 911, 953, 977, 991, 997, 1087, 1097, 1483, 1493, 1801, 1831, 1873, 1901, 1931, 1973, 2287, 2297, 2383, 2393, 2683, 2693, 2803, 2857, 2903, 2957, 3181, 3191, 3583, 3593, 3823, 3847, 3923, 3947, 4483

Offset: 1

Author

Zak Seidov, Sep 05 2010

Keywords

• base
• nonn

Examples

			283 is in the sequence because changing the 8 to a 9 it becomes 293, a different prime. Likewise 293 is also in the sequence.
383 is not in the sequence because changing the 8 to a 9 it becomes 393, which is thrice 131.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A171057.

Programs

Maple

N:= 1000000: # to get all entries <= N
F:= proc(n) local L,R,i;
  if not isprime(n) then return false end if;
  L:= convert(n,base,10);
  R:= subs([8=9,9=8],L);
  if R = L then return false end if;
  isprime(add(R[i]*10^(i-1),i=1..nops(R)))
end proc:
select(F, [seq(2*i+1,i=1..floor((N-1)/2))]);
# Robert Israel, Feb 11 2013

Mathematica

Reap[Do[p = Prime[n]; id = IntegerDigits[p]; id2 = id /. {9 -> 8, 8 -> 9}; If[PrimeQ[fd = FromDigits[id2]]&& fd != p, Sow[p]], {n, 2000}]][[2, 1]]; (* Seidov, corrected by Wouter Meeussen, Feb 10 2013 *)
fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 8] || MemberQ[id, 9]) && PrimeQ[ FromDigits[id /. {8 -> 9, 9 -> 8}] ]]; Select[ Prime@ Range@ 609, fQ] (* Robert G. Wilson v, Sep 06 2010 *)

PARI

is_A175789(n)={my(d=digits(n)); d != (d=apply(t->bitxor(t,t>7),d)) & isprime( sum(i=1, #d, d[i]*10^(#d-i))) & isprime(n)} \\ - M. F. Hasler, Feb 11 2013