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

Author

T. D. Noe, Jun 19 2013

Keywords

• nonn

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

Crossrefs

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

Programs

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]}]]]