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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A007530 (prime quadruples).

Programs

Magma

[Floor((7*n-5)/5): n in [1..100]]; // Zaki Khandaker, Jun 21 2015

Mathematica

a[n_]:=Floor[(7n-5)/5]; Table[a[i],{i,1,30}]; (* Lorenz H. Menke, Jr., Jun 19 2013 *)
LinearRecurrence[{1,0,0,0,1,-1},{0,1,3,4,6,7},80] (* Harvey P. Dale, Jan 24 2025 *)

PARI

a(n)=(7*n-5)\5 \\ Charles R Greathouse IV, Jun 19 2013

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

Extensions

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