A277822 - OEIS

%I #14 Nov 05 2016 07:26:18

%S 0,1,1,2,1,2,3,1,1,2,3,1,4,1,1,2,1,2,3,1,4,1,1,2,5,1,1,2,1,2,3,1,1,2,

%T 3,1,4,1,1,2,5,1,1,2,1,2,3,1,6,1,1,2,1,2,3,1,1,2,3,1,4,1,1,2,1,2,3,1,

%U 4,1,1,2,5,1,1,2,1,2,3,1,6,1,1,2,1,2,3,1,1,2,3,1,4,1,1,2,7,1,1,2,1,2,3,1,1,2,3,1,4,1,1,2,1,2,3,1,4,1,1,2,5

%N a(n) = index of the column where n is located in array A277880.

%C Ordinal transform of A277813.

%C a(n) = 1 + the number of iterations of map k -> A003188(A006068(k)/2) that are required (when starting from k = n) until k is an odious number.

%H Antti Karttunen, <a href="/A277822/b277822.txt">Table of n, a(n) for n = 0..16384</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(0) = 0, for n >= 1, a(n) = 1 + (A010059(n)*A001511(n)).

%F a(0) = 0, for n >= 1, if A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = 1, otherwise a(n) = 1 + a(A003188(A006068(n)/2)).

%F Other identities. For all n >= 1:

%F a(n) = 1 + a(floor(n/2)) when A010060(n) = 0.

%F a(n) = 1+A277808(n).

%o (Scheme, with memoization-macro definec)

%o (definec (A277822 n) (cond ((zero? n) n) ((= 1 (A010060 n)) 1) (else (+ 1 (A277822 (A003188 (/ (A006068 n) 2)))))))

%o ;; Other implementations:

%o (definec (A277822 n) (cond ((zero? n) n) ((= 1 (A010060 n)) 1) (else (+ 1 (A277822 (floor->exact (/ n 2)))))))

%o (define (A277822 n) (+ 1 (* (A010059 n) (A001511 n))))

%Y One more than A277808.

%Y Cf. A000069, A001969, A001511, A003188, A006068, A010059, A010060, A245710, A277813, A277818, A277880.

%K nonn,base

%O 0,4

%A _Antti Karttunen_, Nov 03 2016