A125589 Smallest n-digit base-10 deletable prime.

2, 13, 103, 1013, 10039, 100103, 1000193, 10000931, 100001903, 1000003957, 10000003957, 100000013957, 1000000030957, 10000000301957, 100000000730957, 1000000000730957, 10000000003632979, 100000000007309357

Offset: 1

Author

N. J. A. Sloane, Jan 07 2007

Keywords

• nonn
• base

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, A096243, A096246, A125590.

Programs

Mathematica

b = 10; a = {2}; d = {2, 3, 5, 7};
For[n = 2, n <= 6, n++,
  found = False;
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  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]]];
     If[! found , AppendTo[a, p[[i]]]]; found = True; Break[]]];
]]; a (* Robert Price, Nov 13 2018 *)

Extensions

a(6) - a(8) from Michael Kleber, Jan 08 2007

a(9) - a(14) from Phil Carmody, Jan 09 2007

a(15) - a(18) from Joshua Zucker, Jan 09 2007