A096236 Number of n-digit base-3 deletable primes.

1, 2, 4, 7, 13, 24, 38, 72, 122, 226, 400, 684, 1246, 2381, 4384, 8330, 15839, 30617, 58764, 113987, 221994, 434498, 852036, 1673320, 3296641, 6509179

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. "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 = 3; a = {1}; d = {2};
For[n = 2, n <= 10, 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 *)

Python

from sympy import isprime
from sympy.ntheory.digits import digits
def ok(n, prevset, base=3):
    if not isprime(n): return False
    s = "".join(str(d) for d in digits(n, base)[1:])
    si = (s[:i]+s[i+1:] for i in range(len(s)))
    return any(t[0] != '0' and int(t, base) in prevset for t in si)
def afind(terms):
    s, snxt, base = {2}, set(), 3
    print(len(s), end=", ")
    for n in range(2, terms+1):
        for i in range(base**(n-1), base**n):
            if ok(i, s):
                snxt.add(i)
        s, snxt = snxt, set()
        print(len(s), end=", ")
afind(13) # Michael S. Branicky, Jan 14 2022

Extensions

More terms from John W. Layman, Dec 14 2004

11 more terms from Ryan Propper, Jul 19 2005