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Numbers of the form 2^j + 5^k, for j and k >= 0.

2

`%I #16 Apr 15 2023 14:34:19
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`%S 2,3,5,6,7,9,13,17,21,26,27,29,33,37,41,57,65,69,89,126,127,129,133,
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`%T 141,153,157,189,253,257,261,281,381,513,517,537,626,627,629,633,637,
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`%U 641,657,689,753,881,1025,1029,1049,1137,1149,1649,2049,2053,2073,2173
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`%N Numbers of the form 2^j + 5^k, for j and k >= 0.
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`%C 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
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`%H T. D. Noe, <a href="/A226808/b226808.txt">Table of n, a(n) for n = 1..10000</a>
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`%t 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]}]]]
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`%Y Cf. A004050 (2^j + 3^k), A226806-A226832 (cases to 8^j + 9^k).
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`%K nonn
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`%O 1,1
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`%A _T. D. Noe_, Jun 19 2013
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