A341389 Characteristic function of A158705, nonnegative integers with an odd number of even powers of 2 in their base-2 representation.

0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0

Offset

0

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Index entries for sequences related to binary expansion of n

Formula

a(2n+1) = 1 - a(floor(n/2)) for n >= 0.

a(2n) = a(floor(n/2)) for n > 0 with a(0) = 0.

a(n) = (-1)^n*a(floor(n/4)) + n mod 2 for n > 0 with a(0) = 0.

a(n) = A000035(A139351(n)). - Antti Karttunen, Feb 10 2021

Mathematica

Array[Mod[Total@ IntegerDigits[#, 4], 2] &, 105, 0] (* Michael De Vlieger, Mar 17 2021 *)

Prog

(PARI) A341389(n) = { my(c=0); while(n, c += (n%2); n >>= 2); (c%2); }; \\ Antti Karttunen, Feb 10 2021
(PARI) a(n) = sumdigits(n, 4) % 2; \\ Kevin Ryde, Feb 14 2021

Crossrefs

Cf. A000035, A139351, A158704 (positions of zeros), A158705 (of ones).

Cf. A112539 (complement), A112865 (as +-1).

Sequence in context: A269027 A089809 A165211 * A188027 A359333 A193496

Adjacent sequences: A341386 A341387 A341388 * A341390 A341391 A341392

Keyword

nonn

Author

Mikhail Kurkov, Feb 10 2021

Extensions

Terms corrected by Antti Karttunen, Feb 10 2021

Status

approved