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

Author

Andrey Zabolotskiy, Oct 14 2017

Keywords

• nonn
• easy

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

Crossrefs

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

Programs

PARI

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

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.