A380906 Primes without {3, 5} as digits.

2, 7, 11, 17, 19, 29, 41, 47, 61, 67, 71, 79, 89, 97, 101, 107, 109, 127, 149, 167, 179, 181, 191, 197, 199, 211, 227, 229, 241, 269, 271, 277, 281, 401, 409, 419, 421, 449, 461, 467, 479, 487, 491, 499, 601, 607, 617, 619, 641, 647, 661, 677, 691, 701, 709, 719, 727, 761, 769, 787, 797

Offset: 1

Author

Vincenzo Librandi, Feb 09 2025

Keywords

• base
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 3275 terms from Vincenzo Librandi)
• Index to entries for primes with digits in a given set

Crossrefs

Intersection of A038611 and A038613.

Cf. A000040, A020462, A329760.

Programs

Magma

[p: p in PrimesUpTo(700) | not 3 in Intseq(p) and not 5 in Intseq(p) ];

Mathematica

Select[Prime[Range[120]],DigitCount[#,10,3]==0&&DigitCount[#,10,5]==0&]

PARI

isok(p) = if (isprime(p), my(d=digits(p)); (#select(x->(x==3), d)==0) && (#select(x->(x==5), d)==0)); \\ Michel Marcus, Feb 10 2025

Python

from itertools import count, islice
from sympy import isprime
def A380906_gen(): # generator of terms
    return filter(isprime,(int(oct(n)[2:].translate({51:52,52:54,53:55,54:56,55:57})) for n in count(1)))
A380906_list = list(islice(A380906_gen(),20)) # Chai Wah Wu, Feb 12 2025