A218254 Irregular table, where row n (n >= 0) starts with n, the next term is n-A000120(n), and the successive terms are obtained by repeatedly subtracting the number of 1's in the previous term's binary expansion, until zero is reached, after which the next row starts with one larger n.

0, 1, 0, 2, 1, 0, 3, 1, 0, 4, 3, 1, 0, 5, 3, 1, 0, 6, 4, 3, 1, 0, 7, 4, 3, 1, 0, 8, 7, 4, 3, 1, 0, 9, 7, 4, 3, 1, 0, 10, 8, 7, 4, 3, 1, 0, 11, 8, 7, 4, 3, 1, 0, 12, 10, 8, 7, 4, 3, 1, 0, 13, 10, 8, 7, 4, 3, 1, 0, 14, 11, 8, 7, 4, 3, 1, 0, 15, 11, 8, 7, 4, 3, 1, 0

Offset

0,4

Links

Antti Karttunen, Rows 0..255, flattened

Example

The n-th row (starting indexing from zero) in this irregular table consists of block of length A071542(n)+1: 1,2,3,3,4,4,5,5,... which always ends with zero, as:
0
1,0
2,1,0
3,1,0
4,3,1,0
5,3,1,0
6,4,3,1,0
7,4,3,1,0
The 17th term is 6, which in binary is 110. The 18th term is then 6-2=4.

Prog

(MIT/GNU Scheme)
;; with Antti Karttunen's intseq additions:
(definec (A218254 n) (cond ((< n 2) n) ((not (zero? (A218254 (- n 1)))) (- (A218254 (- n 1)) (A000120 (A218254 (- n 1))))) (else (+ 1 (A218254 (+ 1 (Apos_of_prev_zero (- n 1))))))))
;; The following is an auxiliary function not submitted as a separate entry:
(define Apos_of_prev_zero (compose-funs A213707 -1+ (LEAST-GTE-I 0 0 A213707)))
(PARI) for(n=0, 9, k=n; while(k, print1(k", "); k-=hammingweight(k)); print1("0, ")) \\ Charles R Greathouse IV, Oct 30 2012

Crossrefs

Cf. A218252, A218253. A213707 gives the positions of zeros (i.e. the ending index of each row). A071542, A000120.

The reversed tails of the rows converge towards A179016.

Sequence in context: A110355 A219659 A029293 * A285037 A264422 A376498

Adjacent sequences: A218251 A218252 A218253 * A218255 A218256 A218257

Keyword

nonn,tabf,easy

Author

Nico Brown, Oct 24 2012

Status

approved