A096240 Number of n-digit base-7 deletable primes.

3, 7, 21, 59, 184, 534, 1620, 4889, 15607, 50138, 165569, 551580, 1860565, 6345080

Offset: 1

Author

Michael Kleber, Feb 28 2003

Keywords

• nonn
• base
• more

Comments

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Crossrefs

Cf. A080608, A080603, A096235-A096246.

Programs

Mathematica

b = 7; a = {3}; d = {2, 3, 5};
For[n = 2, n <= 7, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 12 2018 *)

Extensions

9 more terms from Ryan Propper, Jul 19 2005