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 A175886 Numbers that are congruent to {1, 12} mod 13. 13
 1, 12, 14, 25, 27, 38, 40, 51, 53, 64, 66, 77, 79, 90, 92, 103, 105, 116, 118, 129, 131, 142, 144, 155, 157, 168, 170, 181, 183, 194, 196, 207, 209, 220, 222, 233, 235, 246, 248, 259, 261, 272, 274, 285, 287, 298, 300, 311, 313, 324, 326, 337, 339, 350 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Cf. property described by Gary Detlefs in A113801: more generally, these numbers are of the form (2*h*n+(h-4)*(-1)^n-h)/4 (h, n natural numbers), therefore ((2*h*n+(h-4)*(-1)^n-h)/4)^2-1 == 0 (mod h); in this case, a(n)^2-1 == 0 (mod 13). LINKS Bruno Berselli, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA G.f.: x*(1+11*x+x^2)/((1+x)*(1-x)^2). a(n) = (26*n+9*(-1)^n-13)/4. a(n) = -a(-n+1) = a(n-1)+a(n-2)-a(n-3). a(n) = a(n-2)+13. a(n) = 13*A000217(n-1)+1 - 2*sum(a(i), i=1..n-1) for n>1. MATHEMATICA Select[Range[1, 350], MemberQ[{1, 12}, Mod[#, 13]]&] (* Bruno Berselli, Feb 29 2012 *) CoefficientList[Series[(1 + 11 x + x^2) / ((1 + x) (1 - x)^2), {x, 0, 55}], x] (* Vincenzo Librandi, Aug 19 2013 *) LinearRecurrence[{1, 1, -1}, {1, 12, 14}, 60] (* Harvey P. Dale, Oct 23 2015 *) PROG (Haskell) a175886 n = a175886_list !! (n-1) a175886_list = 1 : 12 : map (+ 13) a175886_list -- Reinhard Zumkeller, Jan 07 2012 (MAGMA) [n: n in [1..350] | n mod 13 in [1, 12]]; // Bruno Berselli, Feb 29 2012 (MAGMA) [(26*n+9*(-1)^n-13)/4: n in [1..55]]; // Vincenzo Librandi, Aug 19 2013 (PARI) a(n)=(26*n+9*(-1)^n-13)/4 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A091998, A113801, A005408, A047209, A007310, A047336, A047522, A056020, A090771, A175885, A175887. Cf. A195045 (partial sums). Sequence in context: A229966 A101557 A019292 * A181451 A022326 A307167 Adjacent sequences:  A175883 A175884 A175885 * A175887 A175888 A175889 KEYWORD nonn,easy AUTHOR Bruno Berselli, Oct 08 2010 - Nov 17 2010 STATUS approved

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)