A329761 Primes whose product of decimal digits is a power of 3.

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

1,1

Comments

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)

Formula

{ A000040 } intersect { A174813 }.

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A176870 A089152 A066594 * A167612 A299974 A262433

Adjacent sequences: A329758 A329759 A329760 * A329762 A329763 A329764

Keyword

nonn,base

Author

Alois P. Heinz, Nov 20 2019

Status

approved