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A168671 Numbers that are congruent to {27,36} mod 13. 1

%I

%S 27,36,40,49,53,62,66,75,79,88,92,101,105,114,118,127,131,140,144,153,

%T 157,166,170,179,183,192,196,205,209,218,222,231,235,244,248,257,261,

%U 270,274,283,287,296,300,309,313,322,326,335,339,348,352,361,365,374

%N Numbers that are congruent to {27,36} mod 13.

%C Conjecture: Numbers n such that 36*n^2+72*n+35 is not equal to p*(p+2), where p, p+2 are twin primes.

%C The conjecture is evident, it can be proved as in A169599. [_Bruno Berselli_, Jan 07 2013]

%H Vincenzo Librandi, <a href="/A168671/b168671.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/Sindx_Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F Contribution from _Vincenzo Librandi_, Jul 11 2012: (Start)

%F G.f.: x*(27+9*x-23*x^2)/((1+x)*(1-x)^2).

%F a(n) = (26*n+5*(-1)^n+87)/4.

%F a(n) = a(n-2) +13 = a(n-1) +a(n-2) -a(n-3). (End)

%t Table[(26 n + 5 (-1)^n + 87)/4, {n, 1, 60}] (* _Vincenzo Librandi_, Jul 11 2012 *)

%o (MAGMA) [(26*n +5*(-1)^n+87)/4: n in [1..60]]; // _Vincenzo Librandi_, Jul 11 2012

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Dec 02 2009

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Last modified April 23 06:07 EDT 2014. Contains 240913 sequences.