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A168671
Numbers that are congruent to {1, 10} mod 13.
1
1, 10, 14, 23, 27, 36, 40, 49, 53, 62, 66, 75, 79, 88, 92, 101, 105, 114, 118, 127, 131, 140, 144, 153, 157, 166, 170, 179, 183, 192, 196, 205, 209, 218, 222, 231, 235, 244, 248, 257, 261, 270, 274, 283, 287, 296, 300, 309, 313, 322, 326, 335, 339, 348, 352, 361, 365, 374
OFFSET
1,2
COMMENTS
Conjecture: For no n>1 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]
FORMULA
From Vincenzo Librandi, Jul 11 2012, modified Jul 07 2015: (Start)
G.f.: x*(1+9*x+3*x^2)/((1+x)*(1-x)^2).
a(n) = (26*n+5*(-1)^n-17)/4.
a(n) = a(n-2) +13 = a(n-1) +a(n-2) -a(n-3). (End)
MATHEMATICA
Select[Range[374], MemberQ[{1, 10}, Mod[#, 13]]&] (* Ray Chandler, Jul 08 2015 *)
LinearRecurrence[{1, 1, -1}, {1, 10, 14}, 58] (* Ray Chandler, Jul 08 2015 *)
Rest[CoefficientList[Series[x*(1+9*x+3*x^2)/((1+x)*(1-x)^2), {x, 0, 58}], x]] (* Ray Chandler, Jul 08 2015 *)
CROSSREFS
Sequence in context: A084278 A286843 A069207 * A136197 A071620 A175664
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 02 2009
EXTENSIONS
4 leading terms added. Conjecture clarified. - R. J. Mathar, Jul 07 2015
STATUS
approved