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

4, 16, 94, 585, 3788, 25768, 182762, 1340905, 10135727, 78580647, 622188500, 5018716664

Offset

1,1

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.

Links

Table of n, a(n) for n=1..12.

Daniel Okwor, Deletable primes in bases 3 through 12: code and verification, 2026.

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 *)

Prog

(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

Crossrefs

Cf. A080608, A080603, A096235-A096246.

Sequence in context: A143501 A111291 A050913 * A263565 A131928 A229138

Adjacent sequences: A096240 A096241 A096242 * A096244 A096245 A096246

Keyword

nonn,more,base

Author

Michael Kleber, Feb 28 2003

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

a(12) from Daniel Okwor, Jun 13 2026

Status

approved