A226806 Numbers of the form 2^j + 4^k, for j and k >= 0.

2, 3, 5, 6, 8, 9, 12, 17, 18, 20, 24, 32, 33, 36, 48, 65, 66, 68, 72, 80, 96, 128, 129, 132, 144, 192, 257, 258, 260, 264, 272, 288, 320, 384, 512, 513, 516, 528, 576, 768, 1025, 1026, 1028, 1032, 1040, 1056, 1088, 1152, 1280, 1536, 2048, 2049, 2052, 2064

Offset: 1

Author

T. D. Noe, Jun 19 2013

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Programs

Mathematica

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]}]]]

PARI

ispow2(n)=n>>valuation(n,2)==1
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