A129523 Numbers of the form 2^j +- 2^i for 0 <= i < j, in ascending order.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 24, 28, 30, 31, 32, 33, 34, 36, 40, 48, 56, 60, 62, 63, 64, 65, 66, 68, 72, 80, 96, 112, 120, 124, 126, 127, 128, 129, 130, 132, 136, 144, 160, 192, 224, 240, 248, 252, 254, 255, 256, 257, 258, 260, 264, 272

Offset: 1

Author

Phil Rutschman (phil(AT)rsnsoft.com), Apr 19 2007

Keywords

• nonn

Comments

Positive sums and differences of pairs of distinct powers of two, sorted, with duplicates removed.

Examples

			1 = 2^1 - 2^0; 2 = 2^2 - 2^1; 3 = 2^1 + 2^0 or 2^2 - 2^0; 4 = 2^3 - 2^2; 5 = 2^2 + 2^0.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..1602

Programs

Mathematica

Union[Flatten[Table[{2^n, 2^n - 2^k, 2^n + 2^k}, {n, 8}, {k, 0, n - 1}]]] (* Ivan Neretin, Jul 29 2015 *)

Octave

x=[]; m=12; for i = 0:m; x=[x,2^i-2.^([(i-2):-1:0]),2^i,2^i+2.^([0 :(i-2)])]; end; x

Formula

x(n) = { 2^x - 2^y if x < y }, { 2^x if x = y }, { 2^x + 2^y if x > y} where x = ceiling(sqrt(n)) and y = n - (x-1)^2 - 1.

Union of A018900 and A023758. - M. F. Hasler, Jul 31 2015