A256441 Binary representation of base-(i-1) expansion of -n: replace i-1 with 2 in base-(i-1) expansion of -n.

0, 29, 28, 17, 16, 205, 204, 193, 192, 221, 220, 209, 208, 7437, 7436, 7425, 7424, 7453, 7452, 7441, 7440, 7629, 7628, 7617, 7616, 7645, 7644, 7633, 7632, 7181, 7180, 7169, 7168, 7197, 7196, 7185, 7184, 7373, 7372, 7361, 7360, 7389, 7388, 7377, 7376, 4365

Offset: 0

Author

Paul Tek, Mar 29 2015

Keywords

• base
• nonn
• easy

Comments

Here i = sqrt(-1).

From Jianing Song, Jan 22 2023: (Start)

Also binary representation of base-(-1-i) expansion of -n.

Write out -n in base -4 (A212526), change each digit 0, 1, 2, 3 to 0000, 0001, 1100, 1101 respectively, then interpret as a binary number. (End)

Examples

			a(5) = 205 = 2^7 + 2^6 + 2^3 + 2^2 + 2^0 since (i-1)^7 + (i-1)^6 + (i-1)^3 + (i-1)^2 + (i-1)^0 = -5.
		

Links

• Paul Tek, Table of n, a(n) for n = 0..10000
• Paul Tek, Perl program for this sequence
• Wikipedia, Complex-base system

Crossrefs

Cf. A066321.

Programs

PARI

a(n) = my(v = [-n,0], x=0, digit=0, a, b); while(v!=[0,0], a=v[1]; b=v[2]; v[1]=-2*(a\2)+b; v[2]=-(a\2); x+=(a%2)*2^digit; digit++); x \\ Jianing Song, Jan 22 2023; [a,b] represents the number a + b*(-1+i)

Perl

See Links section.

Formula

For n >= 1, a(4*n-0..3) = 16 * A066321(n) + 0, 1, 12, 13 respectively. - Jianing Song, Jan 22 2023