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

1,2

Comments

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

Links

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

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

Example

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.

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 *)

Prog

(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

Crossrefs

Sequence in context: A333762 A295235 A136490 * A243463 A247805 A164713

Adjacent sequences: A129520 A129521 A129522 * A129524 A129525 A129526

Keyword

nonn

Author

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

Status

approved