A386338 Primes without {2, 8} as digits.

3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 397, 401, 409, 419, 431

Offset: 1

Author

Jason Bard, Jul 19 2025

Keywords

• nonn
• base
• easy

Links

• Jason Bard, Table of n, a(n) for n = 1..10000
• Index to entries for primes with digits in a given set

Crossrefs

Intersection of A038604 and A038616.

Cf. A000040, A329760, A385776.

Programs

Magma

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 3, 4, 5, 6, 7, 9]];

Maple

f:= n-> (l-> add([0, 1, $3..7, 9][l[j]+1]*10^(j-1), j=1..nops(l)))(convert(n, base, 8)):
select(isprime, [seq(f(i), i=0..600)])[];  # Alois P. Heinz, Jul 19 2025

Mathematica

Select[Prime[Range[120]], DigitCount[#, 10, 2] == 0 && DigitCount[#, 10, 8] == 0 &]

PARI

primes_with(, 1, [0, 1, 3, 4, 5, 6, 7, 9]) \\ uses function in A385776

Python

print(list(islice(primes_with("01345679"), 41))) # uses function/imports in A385776