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A037094
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"Sloping binary representation" of Lucas numbers (A000032), slope = +1.
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3
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0, 7, 29, 114, 971, 3695, 14684, 58639, 496705, 1892294, 7518347, 30023387, 258775984, 966632223, 3848859285, 32551146626, 123937019667, 492763242871, 1967451434524, 16666715013959, 63494909959113
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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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).
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CROSSREFS
| Cf. A000032, A037093, A037095, A037099 (same sequence in octal).
Sequence in context: A102485 A049349 A124828 * A118171 A072261 A066744
Adjacent sequences: A037091 A037092 A037093 * A037095 A037096 A037097
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KEYWORD
| nonn,base
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AUTHOR
| Antti Karttunen (His_Firstname.His_Surname(AT)gmail.com), Jan 28 1999. Entry revised Dec 29 2007.
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