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

1,2

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).

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

Mathematica

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

Prog

(Magma) &cat[[7*n, 7*n+5]: n in [0..23]];  // Bruno Berselli, Oct 17 2011
(PARI) a(n) = (14*n + 3*(-1)^n - 11)/4 \\ David Lovler, Sep 11 2022

Crossrefs

Cf. A008589, A017041.

Sequence in context: A306513 A286901 A171490 * A314301 A314302 A314303

Adjacent sequences: A047379 A047380 A047381 * A047383 A047384 A047385

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved