A280997 Primes that have exactly 3 ones in both their binary and ternary expansions.

13, 37, 41, 67, 97, 131, 193, 577, 1033, 1153, 2053, 4129, 8209, 18433, 32771, 32801, 32833, 65539, 133121, 525313, 557057, 1049089, 4194433, 167772161, 268435459

Offset

1,1

Comments

Sequence is likely to be finite. If it exists, a(26) > 10^200. - Robert Israel, Jan 12 2017

Links

Table of n, a(n) for n=1..25.

Example

37 is in the sequence because it is a prime and its binary expansion 100101 and ternary expansion 1101 both have exactly 3 ones.
131 is in the sequence because it is a prime and its binary expansion 10000011 and ternary expansion 11212 both have exactly 3 ones.

Maple

A:= NULL:
for a from 2 to 100 do
  for b from 1 to a-1 do
    p:= 2^a + 2^b + 1;
    if numboccur(1, convert(p, base, 3)) = 3 and isprime(p) then
      A:= A, p
    fi
od od:
A; # Robert Israel, Jan 12 2017

Mathematica

Select[Prime[Range[500000]], Count[IntegerDigits[#, 3], 1] == Count[IntegerDigits[#, 2], 1] == 3 &]

Crossrefs

Cf. A000040, A001363, A007088, A014311, A066196.

Subset of A281004.

Sequence in context: A301591 A301857 A220462 * A185006 A285887 A063913

Adjacent sequences: A280994 A280995 A280996 * A280998 A280999 A281000

Keyword

nonn,base

Author

K. D. Bajpai, Jan 12 2017

Status

approved