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

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, 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, 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

Offset

0,4

Comments

Ordinal transform of A277813.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Index entries for sequences related to binary expansion of n

Formula

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

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)).

Other identities. For all n >= 1:

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

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

Prog

(Scheme, with memoization-macro definec)
(definec (A277822 n) (cond ((zero? n) n) ((= 1 (A010060 n)) 1) (else (+ 1 (A277822 (A003188 (/ (A006068 n) 2)))))))
;; Other implementations:
(definec (A277822 n) (cond ((zero? n) n) ((= 1 (A010060 n)) 1) (else (+ 1 (A277822 (floor->exact (/ n 2)))))))
(define (A277822 n) (+ 1 (* (A010059 n) (A001511 n))))

Crossrefs

One more than A277808.

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

Sequence in context: A131794 A145726 A322984 * A327616 A181631 A348390

Adjacent sequences: A277819 A277820 A277821 * A277823 A277824 A277825

Keyword

nonn,base

Author

Antti Karttunen, Nov 03 2016

Status

approved