A272915 a(n) = n + floor(5*n/6).

0, 1, 3, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 23, 25, 27, 29, 31, 33, 34, 36, 38, 40, 42, 44, 45, 47, 49, 51, 53, 55, 56, 58, 60, 62, 64, 66, 67, 69, 71, 73, 75, 77, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 100, 102, 104, 106, 108, 110, 111, 113, 115, 117, 119

Offset: 0

Author

Bruno Berselli, Jun 15 2016

Keywords

• nonn
• easy

Comments

Equivalently, numbers congruent to {0, 1, 3, 5, 7, 9} mod 11.

In general, n + floor((k-1)*n/k) provides the numbers congruent to {0, 1, 3, 5, ..., 2*k-3} mod (2*k-1) for k>1.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Crossrefs

Cf. similar sequences with formula n+floor((k-1)*n/k): A032766 (k=2), A047220 (k=3), A047392 (k=4), A187318 (k=5).

Programs

Magma

[n+Floor(5*n/6): n in [0..70]];

Mathematica

Table[n + Floor[5 n/6], {n, 0, 70}]

Maxima

makelist(n+floor(5*n/6), n, 0, 70);

PARI

vector(70, n, n--; n+floor(5*n/6))

Python

[n+int(5*n/6) for n in range(70)]

Sage

[n+floor(5*n/6) for n in range(70)];

Formula

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

a(n) = a(n-1) + a(n-6) - a(n-7).

a(6*k + r) = 11*k + 2*r - (1 - (-1)^a(r))/2, with r = 0..5.