A359380 Numbers that are neither multiples of 3 nor of the form 4u+2.

1, 4, 5, 7, 8, 11, 13, 16, 17, 19, 20, 23, 25, 28, 29, 31, 32, 35, 37, 40, 41, 43, 44, 47, 49, 52, 53, 55, 56, 59, 61, 64, 65, 67, 68, 71, 73, 76, 77, 79, 80, 83, 85, 88, 89, 91, 92, 95, 97, 100, 101, 103, 104, 107, 109, 112, 113, 115, 116, 119, 121, 124, 125, 127, 128, 131, 133, 136, 137, 139, 140

Offset: 1

Author

Antti Karttunen, Dec 31 2022

Keywords

• nonn
• easy

Comments

Numbers that are congruent to {1, 4, 5, 7, 8, 11} mod 12. - Amiram Eldar, Jan 24 2023

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1).

Crossrefs

Cf. A187074 (characteristic function).

Cf. also A359375.

Cf. A010892, A057079.

Programs

Mathematica

Select[Range[140], Mod[#, 3] > 0 && Mod[#, 4] != 2 &] (* Amiram Eldar, Dec 31 2022 *)

PARI

isA359380(n) = A187074(n);

Formula

Sum_{n>=1} (-1)^(n+1)/a(n) = (1-1/(4*sqrt(3)))*Pi/3. - Amiram Eldar, Jan 24 2023

From Stefano Spezia, Jul 10 2024: (Start)

G.f.: x*(1 + 2*x - 2*x^2 + 2*x^3 + x^4)/((1 - x)^2*(1 + x^3)).

a(n) = (6*n - 3 - A057079(n+1) + 2*A010892(n+2)/3)/3 for n > 0. (End)