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A227193 Difference of (product of runlengths of 1-bits) and (product of runlengths of 0-bits) in binary representation of n. 3

%I #14 Feb 28 2016 12:12:23

%S 0,0,0,1,-1,0,1,2,-2,-1,0,1,0,1,2,3,-3,-2,-1,0,-1,0,1,2,-1,0,1,3,1,2,

%T 3,4,-4,-3,-2,-1,-3,-1,0,1,-2,-1,0,1,0,1,2,3,-2,-1,0,2,0,1,3,5,0,1,2,

%U 5,2,3,4,5,-5,-4,-3,-2,-5,-2,-1,0,-5,-3,-1,0,-2,0

%N Difference of (product of runlengths of 1-bits) and (product of runlengths of 0-bits) in binary representation of n.

%C The sequence seems to consist of palindromic subsequences centered around each (2^k)-1 and 2^k (with end points near the terms of A000975), which is easily explained by symmetric pairing of binary expansion of n and its complement.

%H Antti Karttunen, <a href="/A227193/b227193.txt">Table of n, a(n) for n = 0..10922</a>

%F a(n) = A227349(n) - A227350(n).

%p a:= proc(n) local i, j, m, r, s; m, r, s:= n, 1, 1;

%p while m>0 do

%p for i from 0 while irem(m, 2, 'h')=0 do m:=h od;

%p for j from 0 while irem(m, 2, 'h')=1 do m:=h od;

%p r, s:= r*j, s*max(i, 1)

%p od; r-s

%p end:

%p seq(a(n), n=0..100); # _Alois P. Heinz_, Jul 11 2013

%t a[n_] := With[{s = Split @ IntegerDigits[n, 2]}, Times @@ Length /@ Select[ s, First[#]==1&] - Times @@ Length /@ Select[s , First[#]==0&]]; Table[ a[n], {n, 0, 100}] (* _Jean-François Alcover_, Feb 28 2016 *)

%o (Scheme) (define (A227193 n) (- (A227349 n) (A227350 n)))

%Y Cf. A145037, A227190.

%K sign

%O 0,8

%A _Antti Karttunen_, Jul 08 2013

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)