%I #50 Sep 11 2022 22:18:43

%S 0,5,7,12,14,19,21,26,28,33,35,40,42,47,49,54,56,61,63,68,70,75,77,82,

%T 84,89,91,96,98,103,105,110,112,117,119,124,126,131,133,138,140,145,

%U 147,152,154,159,161,166,168

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

%C 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

%C Nonnegative k such that k or 4*k + 1 is divisible by 7. - _Bruno Berselli_, Feb 13 2018

%H David Lovler, <a href="/A047382/b047382.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = 7*n - a(n-1) - 9 for n>1, with a(1)=0. - _Vincenzo Librandi_, Aug 05 2010

%F 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

%F From _Bruno Berselli_, Oct 17 2011: (Start)

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

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

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

%F a(n) = ceiling((7/3)*ceiling(3*n/2)). - _Clark Kimberling_, Jul 04 2012

%F E.g.f.: 2 + ((14*x - 11)*exp(x) + 3*exp(-x))/4. - _David Lovler_, Sep 11 2022

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

%o (Magma) &cat[[7*n,7*n+5]: n in [0..23]]; // _Bruno Berselli_, Oct 17 2011

%o (PARI) a(n) = (14*n + 3*(-1)^n - 11)/4 \\ _David Lovler_, Sep 11 2022

%Y Cf. A008589, A017041.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_