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

%I A256441 #21 Jan 22 2023 20:44:59
%S A256441 0,29,28,17,16,205,204,193,192,221,220,209,208,7437,7436,7425,7424,
%T A256441 7453,7452,7441,7440,7629,7628,7617,7616,7645,7644,7633,7632,7181,
%U A256441 7180,7169,7168,7197,7196,7185,7184,7373,7372,7361,7360,7389,7388,7377,7376,4365
%N A256441 Binary representation of base-(i-1) expansion of -n: replace i-1 with 2 in base-(i-1) expansion of -n.
%C A256441 Here i = sqrt(-1).
%C A256441 From _Jianing Song_, Jan 22 2023: (Start)
%C A256441 Also binary representation of base-(-1-i) expansion of -n.
%C A256441 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)
%H A256441 Paul Tek, <a href="/A256441/b256441.txt">Table of n, a(n) for n = 0..10000</a>
%H A256441 Paul Tek, <a href="/A256441/a256441.pl.txt">Perl program for this sequence</a>
%H A256441 Wikipedia, <a href="https://en.wikipedia.org/wiki/Complex-base_system">Complex-base system</a>
%F A256441 For n >= 1, a(4*n-0..3) = 16 * A066321(n) + 0, 1, 12, 13 respectively. - _Jianing Song_, Jan 22 2023
%e A256441 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.
%o A256441 (Perl) See Links section.
%o A256441 (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)
%Y A256441 Cf. A066321.
%K A256441 base,nonn,easy
%O A256441 0,2
%A A256441 _Paul Tek_, Mar 29 2015