A386056 Primes having only {0, 3, 4, 5} as digits.

3, 5, 43, 53, 353, 433, 443, 503, 3343, 3433, 3533, 4003, 5003, 5303, 5333, 5443, 5503, 30403, 30553, 33053, 33343, 33353, 33403, 33503, 33533, 34033, 34303, 34403, 34543, 35053, 35353, 35533, 35543, 40343, 40433, 40543, 43003, 43403, 43543, 44053, 44453, 44533

Offset: 1

Author

Jason Bard, Jul 15 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

Supersequence of A199340, A199345, A260223.

Cf. A000040, A030431, A385776.

Programs

Magma

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

Maple

f:= n-> (l-> add([0, 3, 4, 5][l[j]+1]*10^(j-1), j=1..nops(l)))(convert(n, base, 4)):
select(isprime, [seq(f(i), i=0..695)])[];  # Alois P. Heinz, Jul 15 2025

Mathematica

Select[FromDigits /@ Tuples[{0, 3, 4, 5}, n], PrimeQ]

PARI

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

Python

print(list(islice(primes_with("0345"), 41))) # uses function/imports in A385776