

A218254


Irregular table, where row n (n >= 0) starts with n, the next term is nA000120(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.


12



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
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OFFSET

0,4


LINKS

Antti Karttunen, Rows 0..255, flattened


EXAMPLE

The nth 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 62=4.


PROG

(GNU/MIT 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 (composefuns A213707 1+ (LEASTGTEI 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 A176808
Adjacent sequences: A218251 A218252 A218253 * A218255 A218256 A218257


KEYWORD

nonn,tabf,easy


AUTHOR

Nico Brown, Oct 24 2012


STATUS

approved



