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A168672 Numbers that are congruent to {2,13} mod 17. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 4 17:11 EDT 2020. Contains 334828 sequences. (Running on oeis4.)