A360116 a(n) = 1 if there are no prime factors p of n for which the 2-adic valuation of p-1 is less than that of n-1, otherwise 0.

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

Offset

2

Comments

a(n) = 1 if for all prime factors p of n A007814(p-1) >= A007814(n-1), otherwise 0.

Links

Antti Karttunen, Table of n, a(n) for n = 2..100000

Jon Maiga, Computer-generated formulas for A360116, Sequence Machine.

Index entries for characteristic functions

Formula

a(n) = [A360115(n) = 0], where [ ] is the Iverson bracket.

a(n) = [A333570(n) <= 2] = [A360112(n) <= 2]. (Conjectured by Sequence Machine) - Antti Karttunen, May 14 2025

Mathematica

a[n_] := Module[{v = IntegerExponent[n - 1, 2]}, If[AllTrue[FactorInteger[n][[;; , 1]], IntegerExponent[# - 1, 2] <= v &], 1, 0]]; Array[a, 100, 2] (* Amiram Eldar, Feb 10 2023 *)

Prog

(PARI) A360116(n) = { my(f=factor(n), v=valuation(n-1, 2)); !sum(i=1, #f~, (v < valuation(f[i, 1]-1, 2))); };

Crossrefs

Characteristic function of A360117.

Cf. A333570, A360112, A360113, A360115.

Sequence in context: A239681 A054524 A110471 * A255339 A174854 A103994

Adjacent sequences: A360113 A360114 A360115 * A360117 A360118 A360119

Keyword

nonn

Author

Antti Karttunen, Feb 10 2023

Status

approved