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A037094
"Sloping binary representation" of Lucas numbers (A000032), slope = +1.
3
0, 7, 29, 114, 971, 3695, 14684, 58639, 496705, 1892294, 7518347, 30023387, 258775984, 966632223, 3848859285, 32551146626, 123937019667, 492763242871, 1967451434524, 16666715013959, 63494909959113
OFFSET
0,2
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
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Jan 28 1999. Entry revised Dec 29 2007.
STATUS
approved