

A129523


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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  (x1)^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^i2.^([(i2):1:0]), 2^i, 2^i+2.^([0 :(i2)])]; 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



