A047274 Numbers that are congruent to {0, 1} mod 7.

0, 1, 7, 8, 14, 15, 21, 22, 28, 29, 35, 36, 42, 43, 49, 50, 56, 57, 63, 64, 70, 71, 77, 78, 84, 85, 91, 92, 98, 99, 105, 106, 112, 113, 119, 120, 126, 127, 133, 134, 140, 141, 147, 148, 154, 155, 161, 162, 168, 169

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Nonnegative k such that k or 6*k + 1 is divisible by 7. - Bruno Berselli, Feb 13 2018

Links

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

Crossrefs

Cf. A030308, A135092.

Programs

PARI

forstep(n=0,200,[1,6],print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

Formula

a(n) = 7*n - a(n-1) - 13 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010

From R. J. Mathar, Oct 08 2011: (Start)

a(n) = 7*n/2 - 19/4 - 5*(-1)^n/4.

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

a(n+1) = Sum_{k>=0} A030308(n,k)*A135092(k). - Philippe Deléham, Oct 17 2011

E.g.f.: 6 + ((14*x - 19)*exp(x) - 5*exp(-x))/4. - David Lovler, Aug 31 2022