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

1,1

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

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

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 *)

Prog

(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

Crossrefs

Cf. A080608, A080603, A096235-A096246.

Sequence in context: A233360 A234960 A118850 * A219697 A078668 A038614

Adjacent sequences: A322440 A322441 A322442 * A322444 A322445 A322446

Keyword

nonn,base,easy

Author

Robert Price, Dec 08 2018

Status

approved