A096243 Number of n-digit base-10 deletable primes.

4, 16, 94, 585, 3788, 25768, 182762, 1340905, 10135727, 78580647, 622188500

Offset: 1

Author

Michael Kleber, Feb 28 2003

Keywords

• nonn
• more
• 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.

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 = 10; a = {4}; d = {2, 3, 5, 7};
For[n = 2, n <= 5, 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 13 2018 *)

Python

from sympy import isprime
def ok(n, prevset):
    if not isprime(n): return False
    s = str(n)
    si = (s[:i]+s[i+1:] for i in range(len(s)))
    return any(t[0] != '0' and int(t) in prevset for t in si)
def afind(terms):
    s, snxt = {2, 3, 5, 7}, set()
    print(len(s), end=", ")
    for n in range(2, terms+1):
        for i in range(10**(n-1), 10**n):
            if ok(i, s):
                snxt.add(i)
        s, snxt = snxt, set()
        print(len(s), end=", ")
afind(6) # Michael S. Branicky, Jan 14 2022

Extensions

a(6)-a(9) from Ryan Propper, Jul 19 2005

a(10) from Michael S. Branicky, Jan 14 2022

a(11) from Michael S. Branicky, Jul 06 2023