A037093 - OEIS

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

%S 0,1,3,14,57,229,916,7761,29567,117474,469113,3973641,15138352,

%T 60146777,240187355,2070207870,7733090689,30791909229,260408711716,

%U 991495872825,3942106110215,15739612088946,133333733918417

%N "Sloping binary representation" of Fibonacci numbers, slope = +1.

%F a(n) := Sum(bit_n(A000045(n+i), i)*(2^i), i=0..inf) [ bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2); ]

%F In practice, n can be used as an upper limit instead of infinity.

%e When Fibonacci numbers are written in binary (see A004685), under each other as:

%e 0000000 (0)

%e 0000001 (1)

%e 0000001 (1)

%e 0000010 (2)

%e 0000011 (3)

%e 0000101 (5)

%e 0001000 (8)

%e 0001101 (13)

%e 0010101 (21)

%e 0100010 (34)

%e 0110111 (55)

%e 1011001 (89)

%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), ...00001 (1), ...00011 (3), ...001110 (14), etc. (See A102370 for similar transformation done on nonnegative integers).

%Y Same sequence in octal: A037098. Cf. also: A102370, A000045, A037094-A037095, A036284.

%K nonn,base

%O 0,3

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