%I
%S 13,37,41,67,97,131,193,577,1033,1153,2053,4129,8209,18433,32771,
%T 32801,32833,65539,133121,525313,557057,1049089,4194433,167772161,
%U 268435459
%N Primes that have exactly 3 ones in both their binary and ternary expansions.
%C Sequence is likely to be finite. If it exists, a(26) > 10^200.  _Robert Israel_, Jan 12 2017
%e 37 is in the sequence because it is a prime and its binary expansion 100101 and ternary expansion 1101 both have exactly 3 ones.
%e 131 is in the sequence because it is a prime and its binary expansion 10000011 and ternary expansion 11212 both have exactly 3 ones.
%p A:= NULL:
%p for a from 2 to 100 do
%p for b from 1 to a1 do
%p p:= 2^a + 2^b + 1;
%p if numboccur(1, convert(p,base,3)) = 3 and isprime(p) then
%p A:= A, p
%p fi
%p od od:
%p A; # _Robert Israel_, Jan 12 2017
%t Select[Prime[Range[500000]], Count[IntegerDigits[#, 3], 1] == Count[IntegerDigits[#, 2], 1] == 3 &]
%Y Cf. A000040, A001363, A007088, A014311, A066196.
%Y Subset of A281004.
%K nonn,base
%O 1,1
%A _K. D. Bajpai_, Jan 12 2017
