A037094 "Sloping binary representation" of Lucas numbers (A000032), slope = +1.

0, 7, 29, 114, 971, 3695, 14684, 58639, 496705, 1892294, 7518347, 30023387, 258775984, 966632223, 3848859285, 32551146626, 123937019667, 492763242871, 1967451434524, 16666715013959, 63494909959113

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) := Sum(bit_n(A000032(n+i), i)*(2^i), i=0..inf) [ bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2); ]

In practice, 3n (2n?) can be used as an upper limit instead of infinity.

Example

When Lucas numbers (A000032) are written in binary, under each other as:
0000010 (2)
0000001 (1)
0000011 (3)
0000100 (4)
0000111 (7)
0001011 (11)
0010010 (18)
0011101 (29)
0101111 (47)
1001100 (76)
and one starts collecting their bits from column-0 to SW-direction (from the least to the most significant end), one gets 000... (0), ...00111 (7), ...011101 (29), ...001110010 (114), etc. (See A102370 for similar transformation done on nonnegative integers).

Crossrefs

Cf. A000032, A037093, A037095, A037099 (same sequence in octal).

Sequence in context: A049349 A124828 A296646 * A118171 A072261 A066744

Adjacent sequences: A037091 A037092 A037093 * A037095 A037096 A037097

Keyword

nonn,base

Author

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

Status

approved