A346676 Numbers expressible as 2^x + 3^y where both x and y are positive integers.

5, 7, 11, 13, 17, 19, 25, 29, 31, 35, 41, 43, 59, 67, 73, 83, 85, 89, 91, 97, 113, 131, 137, 145, 155, 209, 245, 247, 251, 259, 265, 275, 283, 307, 337, 371, 499, 515, 521, 539, 593, 731, 733, 737, 745, 755, 761, 793, 857, 985, 1027, 1033, 1051, 1105, 1241

Offset: 1

Author

Keith Backman, Jul 28 2021

Keywords

• nonn

Comments

All terms have the form 6k +- 1.

Crossrefs

Cf. A000079, A000244, A004050.

Programs

PARI

f(x,y) = 2^x + 3^y;
lista(nn) = select(x->(x<=nn), setbinop(f, [1..logint(nn, 2)], [1..logint(nn, 3)])); \\ Michel Marcus, Jul 29 2021

Python

def aupto(lim):
    s, pow3 = set(), 3
    while pow3 < lim:
        for j in range(1, (lim-pow3).bit_length()):
            s.add(2**j + pow3)
        pow3 *= 3
    return sorted(set(s))
print(aupto(1242)) # Michael S. Branicky, Jul 29 2021

Formula

{ A004050 } minus { A000079, A000244 }.