A168672 Numbers that are congruent to {2,13} mod 17.

2, 13, 19, 30, 36, 47, 53, 64, 70, 81, 87, 98, 104, 115, 121, 132, 138, 149, 155, 166, 172, 183, 189, 200, 206, 217, 223, 234, 240, 251, 257, 268, 274, 285, 291, 302, 308, 319, 325, 336, 342, 353, 359, 370, 376, 387, 393, 404, 410, 421, 427, 438, 444, 455, 461, 472, 478, 489

Offset

1,1

Comments

Conjecture: For no term n>2 in the sequence 36*n^2+72*n+35 is equal to p*(p+2), where p, p+2 are twin primes.

The conjecture is evident, it can be proved as in A169599. [Bruno Berselli, Jan 07 2013]

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Jul 11 2012

a(n) = (34*n +5*(-1)^n -21)/4. - Vincenzo Librandi, Jan 06 2013, modified Jul 07 2015

G.f.: x*(2+11*x+4*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 07 2015

Mathematica

Select[Range[489], MemberQ[{2, 13}, Mod[#, 17]]&] (* Ray Chandler, Jul 08 2015 *)
LinearRecurrence[{1, 1, -1}, {2, 13, 19}, 58] (* Ray Chandler, Jul 08 2015 *)
Rest[CoefficientList[Series[x*(2+11*x+4*x^2)/((1+x)*(x-1)^2), {x, 0, 58}], x]] (* Ray Chandler, Jul 08 2015 *)

Crossrefs

Sequence in context: A097234 A122139 A122136 * A297854 A298089 A067208

Adjacent sequences: A168669 A168670 A168671 * A168673 A168674 A168675

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 02 2009

Extensions

5 leading terms added. Conjecture clarified. - R. J. Mathar, Jul 07 2015

Status

approved