A363955 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.

0, 1, 3, 8, 9, 10, 11, 12, 13, 14, 15, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 127, 256, 257, 258, 259

Offset: 1

Author

Jeffrey Shallit, Jun 29 2023

Keywords

• nonn

Examples

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

References

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

Links

• W. Penney, A "binary" system for complex numbers, J. ACM 12 (1965), 247-248.

Crossrefs

Cf. A066321, A271472.

Programs

Mathematica

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

Formula

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