A363955 - OEIS

%I #13 Jun 30 2023 02:48:37

%S 0,1,3,8,9,10,11,12,13,14,15,64,65,67,68,69,71,72,73,74,75,76,77,78,

%T 79,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,

%U 113,115,116,117,119,120,121,122,123,124,125,126,127,256,257,258,259

%N When the base-2 representation of n is interpreted as a Gaussian integer x+yi in base (-1+i), both x and y are nonnegative.

%D J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge, 2003, Section 14.5.

%H W. Penney, <a href="https://dl.acm.org/doi/pdf/10.1145/321264.321274">A "binary" system for complex numbers</a>, J. ACM 12 (1965), 247-248.

%F There is an automaton of 21 states that accepts the base-2 representation of members of this sequence.

%e 9 is in the sequence, since 9 in base 2 is 1001, which is 3+2i in base (-1+i).

%t Select[Range[0, 260], Min[ReIm[FromDigits[IntegerDigits[#, 2], I - 1]]] >= 0 &] (* _Amiram Eldar_, Jun 29 2023 *)

%Y Cf. A066321, A271472.

%K nonn

%O 1,3

%A _Jeffrey Shallit_, Jun 29 2023