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.
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
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
STATUS
approved