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A293668
First differences of A292046.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Andrey Zabolotskiy, Oct 14 2017
STATUS
approved