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Carryless base-2 product (A048720) of run lengths in binary representation of n.
5

%I #8 Apr 15 2017 09:17:37

%S 1,1,1,2,2,1,2,3,3,2,1,2,4,2,3,4,4,3,2,4,2,1,2,3,6,4,2,4,6,3,4,5,5,4,

%T 3,6,4,2,4,6,3,2,1,2,4,2,3,4,8,6,4,8,4,2,4,6,5,6,3,6,8,4,5,6,6,5,4,8,

%U 6,3,6,5,6,4,2,4,8,4,6,8,4,3,2,4,2,1,2,3,6,4,2,4,6,3,4,5,10,8,6,12,8,4,8,12,6,4,2,4,8,4,6,8,12,5,6,12,6,3,6

%N Carryless base-2 product (A048720) of run lengths in binary representation of n.

%H Antti Karttunen, <a href="/A284579/b284579.txt">Table of n, a(n) for n = 0..10922</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F A284581(n) = n - a(n).

%e For n=56, A007088(56) = "111000" in binary, we do carryless multiplication (in base-2) of 3 and 3, thus a(56) = A048720(3,3) = 5.

%o (Scheme) (define (A284579 n) (reduce A048720bi 1 (binexp->runcount1list n))) ;; Where A048720bi is a two-argument function implementing carryless binary product, A048720. For binexp->runcount1list see A167489.

%Y Cf. A000975 (positions of ones).

%Y Cf. A007088, A048720, A284580, A284581.

%Y Differs from A167489 for the first time at n=56, where a(56) = 5, while A167489(56) = 9.

%K nonn,base

%O 0,4

%A _Antti Karttunen_, Apr 14 2017