A215419 Primes that remain prime when a single digit 3 is inserted between any two consecutive digits or as the leading or trailing digit.

7, 11, 17, 31, 37, 73, 271, 331, 359, 373, 673, 733, 1033, 2297, 3119, 3461, 3923, 5323, 5381, 5419, 6073, 6353, 9103, 9887, 18289, 23549, 25349, 31333, 32933, 33349, 35747, 37339, 37361, 37489, 47533, 84299, 92333, 93241, 95093, 98491, 133733, 136333, 139333

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..150

Example

18289 is prime and also 182893, 182839, 182389, 183289, 138289, 318289.

Maple

A215419:=proc(q, x)
local a, b, c, d, i, n, ok;
for n from 1 to q do
  a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;
  a:=ithprime(n); ok:=1;
  for i from 0 to b do
    c:=a+9*10^i*trunc(a/10^i)+10^i*x; if not isprime(c) then ok:=0; break; fi;
  od;
  if ok=1 then print(ithprime(n)); fi;
od; end:
A215419(1000, 3);
# Alternative:
filter:= proc(n) local L, d, k, M;
if not isprime(n) then return false fi;
L:= convert(n, base, 10);
d:= nops(L);
for k from 0 to d do
   M:= [seq(L[i], i=1..k), 3, seq(L[i], i=k+1..d)];
   if not isprime(add(M[i]*10^(i-1), i=1..d+1)) then return false fi;
od;
true
end proc;
select(filter, [seq(i, i=3..2*10^5, 2)]); # Robert Israel, Oct 09 2017

Mathematica

ins@n_:=Insert[IntegerDigits@n, 3, #]&/@Range@(IntegerLength@n+1);
Cases[{#, FromDigits@#&/@ins@#}&/@ Cases[Range[11, 70000], _?PrimeQ], {_, {_?PrimeQ..}}][[All, 1]] (* Hans Rudolf Widmer, Dec 21 2023 *)

Crossrefs

Cf. A215417, A069246, A215420, A215421

Sequence in context: A068674 A156112 A158594 * A107642 A079651 A178386

Adjacent sequences: A215416 A215417 A215418 * A215420 A215421 A215422

Keyword

nonn,base

Author

Paolo P. Lava, Aug 10 2012

Status

approved