A108418 Primes with at least one of each odd digit and no even digits.

13597, 13759, 15739, 15937, 15973, 17359, 17539, 19753, 31957, 37159, 37591, 37951, 39157, 51973, 53197, 53719, 53791, 53917, 57139, 57193, 71359, 71593, 73951, 75193, 75391, 75913, 75931, 79153, 79531, 91573, 91753, 95317, 95713, 95731

Offset: 1

Author

Rick L. Shepherd, Jun 02 2005

Keywords

• base
• nonn

Comments

This is a subsequence of A030096.

No even digits are allowable. Otherwise the first missing terms would be 105379, 105397, 109357, 109537. - Zak Seidov, Nov 24 2013

Links

• Georg Fischer, Table of n, a(n) for n = 1..3000 [recomputed Jul 08 2022; first 390 terms from Carmine Suriano]

Crossrefs

Cf. A030096 (Primes whose digits are all odd), A050288 (Pandigital primes), A108386 (Primes p such that p's set of distinct digits is {1, 3, 7, 9}).

Cf. A232447 (even digits are allowable). - Zak Seidov, Nov 24 2013

Programs

Mathematica

Select[Table[Prime[n],{n,10000}],!ContainsAny[IntegerDigits[#],{0,2,4,6,8}]&&ContainsAll[IntegerDigits[#],{1,3,5,7,9}]&] (* James C. McMahon, Mar 05 2024 *)

Python

from sympy import isprime
from itertools import count, islice, product
def agen():
    for d in count(5):
        for p in product("13579", repeat=d):
            if set(p) != set("13579"): continue
            t = int("".join(p))
            if isprime(t): yield t
print(list(islice(agen(), 40))) # Michael S. Branicky, Jul 08 2022

Extensions

Added missing last term with 5 different digits, Carmine Suriano, Jan 14 2011