A322443 - OEIS

%I #12 Jan 14 2022 01:59:26

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,83,89,101,107,

%T 109,131,137,139,151,157,163,167,179,181,191,197,199,211,223,229,233,

%U 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

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

%C 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.

%C 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.

%H Michael S. Branicky, <a href="/A322443/b322443.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..566 from Robert Price)

%t b = 8; d = {};

%t p = Select[Range[2, 10000], PrimeQ[#] &];

%t For[i = 1, i <= Length[p], i++,

%t c = IntegerDigits[p[[i]], b];

%t If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];

%t For[j = 1, j <= Length[c], j++,

%t t = Delete[c, j];

%t If[t[[1]] == 0, Continue[]];

%t If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]];

%t d (* _Robert Price_, Dec 08 2018 *)

%o (Python)

%o from sympy import isprime

%o def ok(n):

%o     if not isprime(n): return False

%o     if n < 8: return True

%o     o = oct(n)[2:]

%o     oi = (o[:i]+o[i+1:] for i in range(len(o)))

%o     return any(t[0] != '0' and ok(int(t, 8)) for t in oi)

%o print([k for k in range(492) if ok(k)]) # _Michael S. Branicky_, Jan 13 2022

%Y Cf. A080608, A080603, A096235-A096246.

%K nonn,base,easy

%O 1,1

%A _Robert Price_, Dec 08 2018