A306085 Primes which have an even decimal digit and remain prime after all even digits are removed.

23, 43, 47, 67, 83, 101, 103, 107, 109, 127, 149, 163, 167, 181, 211, 223, 227, 263, 271, 283, 307, 347, 367, 419, 431, 443, 463, 467, 479, 487, 503, 509, 523, 563, 569, 607, 613, 617, 619, 631, 643, 647, 653, 659, 673, 683, 701, 709, 743, 761, 769, 811, 823, 827, 853, 859, 863, 883, 887, 907

Offset

1,1

Comments

A proper subset of A306084.

Links

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

Example

101 is a member of the sequence because it has an even digit, 0, and with its removal, the resulting number 11 is a prime.

Maple

filter:= proc(n) local L, Lp;
  if not isprime(n) then return false fi;
  L:= convert(n, base, 10);
  Lp:= subs([0=NULL, 2=NULL, 4=NULL, 6=NULL, 8=NULL], L);
  if L = Lp then return false fi;
  isprime(add(Lp[i]*10^(i-1), i=1..nops(Lp)))
end proc:
select(filter, [seq(n, n=11..1000, 2)]); # Robert Israel, Jul 04 2018

Mathematica

fQ[n_] := Block[{id = IntegerDigits@ n}, Select[id, EvenQ] != {} && PrimeQ[ FromDigits[ Select[id, OddQ]] ]]; Select[Prime@ Range@ 160, fQ]

Prog

(PARI) isok(p) = isprime(p) && (d=digits(p)) && #select(x->!(x%2), d) && isprime(fromdigits(select(x->(x % 2), d))); \\ Michel Marcus, Jun 22 2018

Crossrefs

Cf. A306084, A306086.

Sequence in context: A304390 A309533 A331342 * A037137 A340136 A154530

Adjacent sequences: A306082 A306083 A306084 * A306086 A306087 A306088

Keyword

nonn,base

Author

Zak Seidov and Robert G. Wilson v, Jun 20 2018

Status

approved