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

Offset: 0

Author

N. J. A. Sloane, Aug 10 2019

Keywords

• sign
• base

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

Crossrefs

Cf. A003816, A309529, A309214, A309215, A309216, A309218.

Programs

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];
od:
a; # A309217
b; # A309218