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A309217

The sequence is {a(n), n>=0}, the concatenation of the binary expansions of the absolute values |a(n)| is {b(n), n>=0}; start with a(0)=0; thereafter a(n) = a(n-1)+n if b(n-1)=0, otherwise a(n) = a(n-1)-n.

0, 1, -1, -4, -8, -3, 3, -4, 4, 13, 23, 12, 0, -13, -27, -42, -26, -9, -27, -8, 12, -9, -31, -8, -32, -57, -31, -58, -86, -115, -145, -176, -144, -111, -77, -112, -148, -111, -149, -188, -228, -187, -229, -272, -316, -271, -317, -270, -318, -269, -319, -370, -318, -371, -317, -372, -316

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OFFSET

0,4

COMMENTS

The b-sequence (A309218) is 0; 1; 1; 1, 0, 0; 1, 0, 0, 0; 1, 1; 1, 1; 1, 0, 0; 1, 0, 0; ... Note that we write the binary expansions in human order (as in A309216), with high-order bits on the left.

This is a base-2 analog of A309216.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

MAPLE

t:=0;

a:=[0]; b:=[]; M:=100;

for i from 1 to M do

v1:=convert(abs(t), base, 2); L:=nops(v1);

v2:=[seq(v1[L-i+1], i=1..L)];

b:=[op(b), op(v2)];

if (b[i] mod 2) = 0 then t:=t+i else t:=t-i; fi;

a:=[op(a), t];