A226806 - OEIS

%I #10 May 02 2023 06:21:26

%S 2,3,5,6,8,9,12,17,18,20,24,32,33,36,48,65,66,68,72,80,96,128,129,132,

%T 144,192,257,258,260,264,272,288,320,384,512,513,516,528,576,768,1025,

%U 1026,1028,1032,1040,1056,1088,1152,1280,1536,2048,2049,2052,2064

%N Numbers of the form 2^j + 4^k, for j and k >= 0.

%C Conjecture: Any integer n > 1 not equal to 4 can be written as a sum of distinct terms of the current sequence with no summand dividing another. - _Zhi-Wei Sun_, May 01 2023

%H T. D. Noe, <a href="/A226806/b226806.txt">Table of n, a(n) for n = 1..10000</a>

%t a = 2; b = 4; mx = 3000; Union[Flatten[Table[a^n + b^m, {m, 0, Log[b, mx]}, {n, 0, Log[a, mx - b^m]}]]]

%o (PARI) ispow2(n)=n>>valuation(n,2)==1

%o is(n)=my(h=hammingweight(n)); if(h>2, 0, h==2, valuation(n,2)%2==0 || logint(n,2)%2==0, h==1 && valuation(n,2)%2) \\ _Charles R Greathouse IV_, Aug 29 2016

%Y Cf. A004050 (2^j + 3^k), A226807-A226832 (cases to 8^j + 9^k).

%K nonn

%O 1,1

%A _T. D. Noe_, Jun 19 2013