A047382 Numbers that are congruent to {0, 5} mod 7.

0, 5, 7, 12, 14, 19, 21, 26, 28, 33, 35, 40, 42, 47, 49, 54, 56, 61, 63, 68, 70, 75, 77, 82, 84, 89, 91, 96, 98, 103, 105, 110, 112, 117, 119, 124, 126, 131, 133, 138, 140, 145, 147, 152, 154, 159, 161, 166, 168

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Except for the first term, numbers m such that 36*m^2 + 72*m + 35 = (6*m+5)*(6*m+7) is not of the form p*(p+2), with p prime. - Vincenzo Librandi, Aug 05 2010

Nonnegative k such that k or 4*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. A008589, A017041.

Programs

Magma

&cat[[7*n,7*n+5]: n in [0..23]];  // Bruno Berselli, Oct 17 2011

Mathematica

{#, 5 + #} &/@ (7 Range[0, 30]) // Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 5, 7}, 60] (* Harvey P. Dale, Dec 01 2016 *)

PARI

a(n) = (14*n + 3*(-1)^n - 11)/4 \\ David Lovler, Sep 11 2022

Formula

a(n) = 7*n - a(n-1) - 9 for n>1, with a(1)=0. - Vincenzo Librandi, Aug 05 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=5 and b(k)=A005009(k-1)=7*2^(k-1) for k>0. - Philippe Deléham, Oct 17 2011

From Bruno Berselli, Oct 17 2011: (Start)

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

a(n) = (14*n + 3*(-1)^n - 11)/4.

a(-n) = -A047352(n+2). (End)

a(n) = ceiling((7/3)*ceiling(3*n/2)). - Clark Kimberling, Jul 04 2012

E.g.f.: 2 + ((14*x - 11)*exp(x) + 3*exp(-x))/4. - David Lovler, Sep 11 2022