A329761 Primes having only {1, 3, 9} as digits.

3, 11, 13, 19, 31, 113, 131, 139, 191, 193, 199, 311, 313, 331, 911, 919, 991, 1193, 1319, 1399, 1913, 1931, 1933, 1993, 1999, 3119, 3191, 3313, 3319, 3331, 3391, 3911, 3919, 3931, 9133, 9199, 9311, 9319, 9391, 9931, 11113, 11119, 11131, 11311, 11393, 11399

Offset: 1

Author

Alois P. Heinz, Nov 20 2019

Keywords

• nonn
• base

Comments

Original name was: Primes whose product of decimal digits is a power of 3.

Primes whose digit set is a subset of {1,3,9}.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000
• Marianne Freiberger, Primes without 7s.
• James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
• James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
• Index to entries for primes with digits in a given set

Crossrefs

Subsequence of A030096.

Cf. A000040, A000244, A007954, A020457, A174813.

Programs

Magma

[p: p in PrimesUpTo(12000) | Set(Intseq(p)) subset [1,3,9]]; // Vincenzo Librandi, Jan 02 2019

Mathematica

Select[Prime[Range[1500]],IntegerQ[Log[3,Times@@IntegerDigits[#]]]&] (* or *) Table[Select[FromDigits/@Tuples[{1,3,9},n],PrimeQ],{n,5}]// Flatten (* Harvey P. Dale, Dec 31 2019 *)

Formula

{ A000040 } intersect { A174813 }.

a(n) in { A000040 } and A007954(a(n)) in { A000244 }.

Extensions

Name changed by Sean A. Irvine, Jul 20 2025