A226807 Numbers of the form 3^j + 4^k, for j and k >= 0.

2, 4, 5, 7, 10, 13, 17, 19, 25, 28, 31, 43, 65, 67, 73, 82, 85, 91, 97, 145, 244, 247, 257, 259, 265, 283, 307, 337, 499, 730, 733, 745, 793, 985, 1025, 1027, 1033, 1051, 1105, 1267, 1753, 2188, 2191, 2203, 2251, 2443, 3211, 4097, 4099, 4105, 4123, 4177, 4339

Offset

1,1

Comments

Conjecture: Each integer n > 8 can be written as a sum of finitely many numbers of the form 3^a + 4^b (a,b >= 0) with no one dividing another. This has been verified for all n <= 1500. - Zhi-Wei Sun, Apr 18 2023

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Mathematica

a = 3; b = 4; mx = 5000; Union[Flatten[Table[a^n + b^m, {m, 0, Log[b, mx]}, {n, 0, Log[a, mx - b^m]}]]]

Crossrefs

Cf. A004050 (2^j + 3^k), A226806-A226832 (cases to 8^j + 9^k).

Sequence in context: A036559 A083022 A279022 * A211523 A340246 A062463

Adjacent sequences: A226804 A226805 A226806 * A226808 A226809 A226810

Keyword

nonn

Author

T. D. Noe, Jun 19 2013

Status

approved