A037093 "Sloping binary representation" of Fibonacci numbers, slope = +1.

0, 1, 3, 14, 57, 229, 916, 7761, 29567, 117474, 469113, 3973641, 15138352, 60146777, 240187355, 2070207870, 7733090689, 30791909229, 260408711716, 991495872825, 3942106110215, 15739612088946, 133333733918417

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) := Sum(bit_n(A000045(n+i), i)*(2^i), i=0..inf) [ bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2); ]

In practice, n can be used as an upper limit instead of infinity.

Example

When Fibonacci numbers are written in binary (see A004685), under each other as:
0000000 (0)
0000001 (1)
0000001 (1)
0000010 (2)
0000011 (3)
0000101 (5)
0001000 (8)
0001101 (13)
0010101 (21)
0100010 (34)
0110111 (55)
1011001 (89)
and one starts collecting their bits from column-0 to SW-direction (from the least to the most significant end), one gets 000... (0), ...00001 (1), ...00011 (3), ...001110 (14), etc. (See A102370 for similar transformation done on nonnegative integers).

Crossrefs

Same sequence in octal: A037098. Cf. also: A102370, A000045, A037094-A037095, A036284.

Sequence in context: A052412 A353095 A037793 * A135926 A015523 A127363

Adjacent sequences: A037090 A037091 A037092 * A037094 A037095 A037096

Keyword

nonn,base

Author

Antti Karttunen, Jan 28 1999. Entry revised Dec 29 2007.

Status

approved