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A322443 Base-8 deletable primes (written in base 10). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 20:08 EDT 2022. Contains 353957 sequences. (Running on oeis4.)