A322443 Base-8 deletable primes (written in base 10).

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 83, 89, 101, 107, 109, 131, 137, 139, 151, 157, 163, 167, 179, 181, 191, 197, 199, 211, 223, 229, 233, 239, 251, 269, 277, 293, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 421, 431, 443, 461, 467, 479, 491

Offset: 1

Author

Robert Price, Dec 08 2018

Keywords

• nonn
• base
• easy

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

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..566 from Robert Price)

Crossrefs

Cf. A080608, A080603, A096235-A096246.

Programs

Mathematica

b = 8; d = {};
p = Select[Range[2, 10000], PrimeQ[#] &];
For[i = 1, i <= Length[p], i++,
c = IntegerDigits[p[[i]], b];
If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];
For[j = 1, j <= Length[c], j++,
t = Delete[c, j];
If[t[[1]] == 0, Continue[]];
If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]];
d (* Robert Price, Dec 08 2018 *)

Python

from sympy import isprime
def ok(n):
    if not isprime(n): return False
    if n < 8: return True
    o = oct(n)[2:]
    oi = (o[:i]+o[i+1:] for i in range(len(o)))
    return any(t[0] != '0' and ok(int(t, 8)) for t in oi)
print([k for k in range(492) if ok(k)]) # Michael S. Branicky, Jan 13 2022