A353314 If n is of the form 3k, then a(n) = n, and if n is of the form 3k+r, with r = 1 or 2, then a(n) = 5*k + 3 + r.

0, 4, 5, 3, 9, 10, 6, 14, 15, 9, 19, 20, 12, 24, 25, 15, 29, 30, 18, 34, 35, 21, 39, 40, 24, 44, 45, 27, 49, 50, 30, 54, 55, 33, 59, 60, 36, 64, 65, 39, 69, 70, 42, 74, 75, 45, 79, 80, 48, 84, 85, 51, 89, 90, 54, 94, 95, 57, 99, 100, 60, 104, 105, 63, 109, 110, 66, 114, 115, 69, 119, 120, 72, 124, 125, 75, 129, 130

Offset: 0

Author

Antti Karttunen, Apr 14 2022

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Nicholas Drozd, A Busy Beaver Champion Derived from Scratch
• Nicholas Drozd, Feedback to Doron Zeilberger's opinion #155, Jan. 4, 2022.
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A353313 (variant), A349876 (the first multiple of 3 reached when iterating this sequence), A349877 (number of iterations to reach the first multiple of 3), A353327 (A102899).

Programs

Mathematica

Array[If[#2 == 0, #1, 5 #1 + 3 + #2 & @@ QuotientRemainder[#1, 3]] & @@ {#, Mod[#, 3]} &, 78, 0] (* Michael De Vlieger, Apr 14 2022 *)

PARI

A353314(n) = { my(r=(n%3)); if(!r,n,((5*((n-r)/3)) + r + 3)); };

Formula

a(n) = n + A353327(n) = n + A102899(3+n).

From Chai Wah Wu, Jul 27 2022: (Start)

a(n) = 2*a(n-3) - a(n-6) for n > 5.

G.f.: x*(x^3 + 3*x^2 + 5*x + 4)/(x^6 - 2*x^3 + 1). (End)