A225875 We write the 1 + 4*k numbers once and twice the others.

1, 2, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43

Offset: 1

Author

José María Grau Ribas, May 19 2013

Keywords

• nonn
• easy

Comments

First differences are periodic with period 7.

Links

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

Crossrefs

Cf. A132270.

Programs

Mathematica

t = {}; Do[If[Mod[n, 4] == 1, AppendTo[t, n], AppendTo[t, {n, n}]], {n, 50}]; Flatten[t] (* T. D. Noe, May 23 2013 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1},{1, 2, 2, 3, 3, 4, 4, 5},74] (* Ray Chandler, Aug 26 2015 *)
Table[If[Mod[n, 4] == 1, n, {n, n}], {n, 50}] // Flatten (* or *) Drop[ Flatten[ Table[{n,n},{n,50}]],{1,-1,8}] (* Harvey P. Dale, Feb 03 2019 *)

Formula

a(n+1) = 1 + 4*floor(n/7) + [0,1,1,2,2,3,3].

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

a(n) = n - floor(3*n/7). - Wesley Ivan Hurt, Sep 29 2017

Extensions

Corrected, extended, and edited by Ralf Stephan, May 20 2013