A047299 Numbers that are congruent to {0, 1, 3, 4, 6} mod 7.

0, 1, 3, 4, 6, 7, 8, 10, 11, 13, 14, 15, 17, 18, 20, 21, 22, 24, 25, 27, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 50, 52, 53, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, 70, 71, 73, 74, 76, 77, 78

Offset

1,3

Comments

Nonnegative m such that floor(k*m^2/7) = k*floor(m^2/7), where k = 2 or 3. [Bruno Berselli, Dec 03 2015]

For k > 1 (A007530(k+1) - A007530(k))/30 is a term in this sequence. - Hugo Pfoertner, May 29 2020

Links

Table of n, a(n) for n=1..57.

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

Formula

G.f.: x^2*(1+2*x+x^2+2*x^3+x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

a(n) = floor((7n-5)/5). - Lorenz H. Menke, Jr., Jun 19 2013

Mathematica

a[n_]:=Floor[(7n-5)/5]; Table[a[i], {i, 1, 30}]; (* Lorenz H. Menke, Jr., Jun 19 2013 *)

Prog

(PARI) a(n)=(7*n-5)\5 \\ Charles R Greathouse IV, Jun 19 2013
(Magma) [Floor((7*n-5)/5): n in [1..100]]; // Zaki Khandaker, Jun 21 2015

Crossrefs

Cf. A007530 (prime quadruples).

Sequence in context: A247987 A062975 A276218 * A186159 A184578 A022846

Adjacent sequences: A047296 A047297 A047298 * A047300 A047301 A047302

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Formula and programs adapted to offset 1 by Michel Marcus, May 30 2020

Status

approved