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

1,1

Comments

All terms have the form 6k +- 1.

Links

Table of n, a(n) for n=1..55.

Formula

{ A004050 } minus { A000079, A000244 }.

Prog

(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

Crossrefs

Cf. A000079, A000244, A004050.

Sequence in context: A216524 A128824 A098420 * A309726 A093495 A093496

Adjacent sequences: A346673 A346674 A346675 * A346677 A346678 A346679

Keyword

nonn

Author

Keith Backman, Jul 28 2021

Status

approved