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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A171057.

Sequence in context: A253432 A218977 A253439 * A157747 A253156 A139649

Adjacent sequences: A175786 A175787 A175788 * A175790 A175791 A175792

Keyword

base,nonn

Author

Zak Seidov, Sep 05 2010

Status

approved