A096238 Number of n-digit base-5 deletable primes.

2, 6, 14, 32, 69, 156, 377, 855, 2072, 5131, 12922, 32619, 83945, 217305, 571560, 1517012, 4056107

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 = 5; a = {2}; d = {2, 3};
For[n = 2, n <= 8, 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

12 more terms from Ryan Propper, Jul 19 2005