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A226808
Numbers of the form 2^j + 5^k, for j and k >= 0.
2
2, 3, 5, 6, 7, 9, 13, 17, 21, 26, 27, 29, 33, 37, 41, 57, 65, 69, 89, 126, 127, 129, 133, 141, 153, 157, 189, 253, 257, 261, 281, 381, 513, 517, 537, 626, 627, 629, 633, 637, 641, 657, 689, 753, 881, 1025, 1029, 1049, 1137, 1149, 1649, 2049, 2053, 2073, 2173
OFFSET
1,1
COMMENTS
Conjecture: Each integer n > 4 can be written as a_1 + ... + a_k, where a_1,...,a_k are numbers of the form 2^a + 5^b (a,b>=0) (i.e., terms of the current sequence) with no one dividing another. This has been verified for n = 5..1200. - Zhi-Wei Sun, Apr 14 2023
MATHEMATICA
a = 2; b = 5; mx = 3000; 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: A074780 A292938 A056900 * A096594 A100693 A030159
KEYWORD
nonn
AUTHOR
T. D. Noe, Jun 19 2013
STATUS
approved