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"Sloping binary representation" of Lucas numbers (A000032), slope = +1.
3

%I #7 Mar 31 2012 14:02:29

%S 0,7,29,114,971,3695,14684,58639,496705,1892294,7518347,30023387,

%T 258775984,966632223,3848859285,32551146626,123937019667,492763242871,

%U 1967451434524,16666715013959,63494909959113

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

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

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

%e When Lucas numbers (A000032) are written in binary, under each other as:

%e 0000010 (2)

%e 0000001 (1)

%e 0000011 (3)

%e 0000100 (4)

%e 0000111 (7)

%e 0001011 (11)

%e 0010010 (18)

%e 0011101 (29)

%e 0101111 (47)

%e 1001100 (76)

%e 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).

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

%K nonn,base

%O 0,2

%A _Antti Karttunen_, Jan 28 1999. Entry revised Dec 29 2007.