A096245 Number of n-digit base-12 deletable primes.

5, 25, 186, 1398, 11500, 99074, 893062, 8352961, 80564801

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 0's 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 = 12; a = {5}; d = {2, 3, 5, 7, 11};
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
from sympy.ntheory.digits import digits
def strmap(d):
    return str(d) if d < 10 else "ABCDEFGHIJKLMNOPQRSTUVWXYZ"[d-10]
def ok(n, prevset, base=12): # works for bases 2-36
    if not isprime(n): return False
    s = "".join(strmap(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, base=12): # works for bases 3-36
    s = set([p for p in range(1, base) if isprime(p)])
    alst, snxt = [len(s)], set()
    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(6) # Michael S. Branicky, Jan 17 2022

Extensions

a(6)-a(8) from Ryan Propper, Jul 19 2005

Edited by Charles R Greathouse IV, Aug 03 2010

a(9) from Michael S. Branicky, Jan 17 2022