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A277822 a(n) = index of the column where n is located in array A277880.

%I A277822 #14 Nov 05 2016 07:26:18
%S A277822 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 A277822 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 A277822 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 A277822 a(n) = index of the column where n is located in array A277880.
%C A277822 Ordinal transform of A277813.
%C A277822 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 A277822 Antti Karttunen, <a href="/A277822/b277822.txt">Table of n, a(n) for n = 0..16384</a>
%H A277822 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A277822 a(0) = 0, for n >= 1, a(n) = 1 + (A010059(n)*A001511(n)).
%F A277822 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 A277822 Other identities. For all n >= 1:
%F A277822 a(n) = 1 + a(floor(n/2)) when A010060(n) = 0.
%F A277822 a(n) = 1+A277808(n).
%o A277822 (Scheme, with memoization-macro definec)
%o A277822 (definec (A277822 n) (cond ((zero? n) n) ((= 1 (A010060 n)) 1) (else (+ 1 (A277822 (A003188 (/ (A006068 n) 2)))))))
%o A277822 ;; Other implementations:
%o A277822 (definec (A277822 n) (cond ((zero? n) n) ((= 1 (A010060 n)) 1) (else (+ 1 (A277822 (floor->exact (/ n 2)))))))
%o A277822 (define (A277822 n) (+ 1 (* (A010059 n) (A001511 n))))
%Y A277822 One more than A277808.
%Y A277822 Cf. A000069, A001969, A001511, A003188, A006068, A010059, A010060, A245710, A277813, A277818, A277880.
%K A277822 nonn,base
%O A277822 0,4
%A A277822 _Antti Karttunen_, Nov 03 2016