A281004 Numbers with exactly 3 ones in both binary and ternary representations.

13, 37, 41, 49, 67, 97, 131, 133, 145, 193, 259, 265, 273, 289, 385, 517, 529, 577, 1027, 1029, 1033, 1041, 1153, 1281, 2053, 2057, 4101, 4105, 4113, 4129, 4161, 6145, 8195, 8197, 8209, 8225, 8257, 8321, 8449, 8705, 10241, 16449, 17409, 18433, 20481, 24577, 32771, 32777, 32785, 32801, 32833, 32897

Offset: 1

Author

Robert Israel, Jan 12 2017

Keywords

• nonn
• base

Comments

Intersection of A014311 and A023694.

All terms are odd, since n == A062756(n) (mod 2).

It is likely that a(136) = 1099528404993 is the last term. The next term, if any, is greater than 10^200.

Examples

			a(4) = 49 = 110001_2 = 1211_3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..136

Crossrefs

Cf. A014311, A023694, A062756. Contains A280997.

Programs

Maple

R:= NULL: count:= 0:
for a from 2 while count < 136 do
  for b from 1 to a-1  do
    p:= 2^a + 2^b + 1;
    if numboccur(1, convert(p,base,3)) = 3 then
      count:= count+1;
      R:= R, p;
    fi
od od:
R;