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A329761
Primes whose product of decimal digits is a power of 3.
2
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
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
KEYWORD
nonn,base
AUTHOR
Alois P. Heinz, Nov 20 2019
STATUS
approved