A359374 Parity of A252463(n).

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

Offset

1

Comments

Period 12: repeat [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]. - Amiram Eldar, Jan 24 2023

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

Index entries for linear recurrences with constant coefficients, signature (0,-1,0,0,0,1,0,1).

Formula

a(n) = A000035(A252463(n)).

For n >= 1, a(n) = 1 - A359379(n).

Mathematica

a[n_] := If[Mod[n, 6] == 3 || Mod[n, 4] == 0, 0, 1]; Array[a, 100] (* Amiram Eldar, Jan 24 2023 *)

Prog

(PARI) A359374(n) = !(((n%2)&&!(n%3))||!(n%4));
(PARI)
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A252463(n) = if(!(n%2), n/2, A064989(n));
A359374(n) = (A252463(n)%2);

Crossrefs

Characteristic function of A359375, whose complement A359376 gives the positions of zeros.

Cf. A000035, A064989, A252463, A359379 (one's complement).

Sequence in context: A127015 A281114 A286749 * A188192 A068432 A134668

Adjacent sequences: A359371 A359372 A359373 * A359375 A359376 A359377

Keyword

nonn

Author

Antti Karttunen, Dec 31 2022

Status

approved