A293668 First differences of A292046.

1, 2, 3, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,2

Comments

a(n) is also the length of n-th run of consecutive integers in the complement of A292046, starting from the 1st run "4, 5".

This sequence is invariant under the following transform: subtract 1 from every term, eliminate zeros. Other sequences with this property include A001511 and other generalized ruler functions, A002260, A272729.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Formula

a(0) = 1, a(n) = A292046(n+1)-A292046(n) for n>0.

If n = 2^k, a(n) = a(k)+1; otherwise a(n) = 1.

a(n) = A255308(n) + 1.

a(n) = O(log*(n)), where log* is the iterated logarithm. More precisely, a(n) <= A230864(n+1)+1.

Prog

(PARI) A293668(n) = { my(k=1); while(n && !bitand(n, n-1), n = valuation(n, 2); k++); (k); }; \\ Antti Karttunen, Sep 30 2018

Crossrefs

Cf. A001511, A002260, A230864, A255308, A272729, A292046.

Sequence in context: A152832 A211343 A039661 * A214684 A268727 A325542

Adjacent sequences: A293665 A293666 A293667 * A293669 A293670 A293671

Keyword

nonn,easy

Author

Andrey Zabolotskiy, Oct 14 2017

Status

approved