cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A037094 #9 Jul 08 2025 21:04:19
%S A037094 0,7,29,114,971,3695,14684,58639,496705,1892294,7518347,30023387,
%T A037094 258775984,966632223,3848859285,32551146626,123937019667,492763242871,
%U A037094 1967451434524,16666715013959,63494909959113
%N A037094 "Sloping binary representation" of Lucas numbers (A000032), slope = +1.
%F A037094 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 A037094 In practice, 3n (2n?) can be used as an upper limit instead of infinity.
%e A037094 When Lucas numbers (A000032) are written in binary, under each other as:
%e A037094 0000010 (2)
%e A037094 0000001 (1)
%e A037094 0000011 (3)
%e A037094 0000100 (4)
%e A037094 0000111 (7)
%e A037094 0001011 (11)
%e A037094 0010010 (18)
%e A037094 0011101 (29)
%e A037094 0101111 (47)
%e A037094 1001100 (76)
%e A037094 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 A037094 Cf. A000032, A037093, A037095, A037099 (same sequence in octal).
%K A037094 nonn,base
%O A037094 0,2
%A A037094 _Antti Karttunen_, Jan 28 1999
%E A037094 Entry revised Dec 29 2007