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 A295340 Numbers congruent to 11 or 13 mod 15. 1
 11, 13, 26, 28, 41, 43, 56, 58, 71, 73, 86, 88, 101, 103, 116, 118, 131, 133, 146, 148, 161, 163, 176, 178, 191, 193, 206, 208, 221, 223, 236, 238, 251, 253, 266, 268, 281, 283, 296, 298, 311, 313, 326, 328, 341, 343, 356, 358, 371, 373, 386, 388, 401, 403, 416, 418, 431, 433 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Includes every prime and twin prime (as pairs of consecutive primes) congruent to 11 or 13 mod 30. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = (1/4)*(-1)^n*(3*(-1)^n*(10*n + 1) - 11) for n > 0. From Colin Barker, Dec 07 2017: (Start) G.f.: x*(11 + 2*x + 2*x^2) / ((1 - x)^2*(1 + x)). a(n) = (15*n - 4) / 2 for n even. a(n) = (15*n + 7) / 2 for n odd. a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3. (End) a(n) = (1/4)*(33 + 11*(-1)^(n-1) + 30*(n-1)). - Paolo P. Lava, Dec 11 2017 a(n) = ceiling(15*n/2) + 5*(n mod 2) - 2 for n > 0. - Mikk Heidemaa, Sep 06 2018 a(n + 2) = a(n) + 15. - David A. Corneth, Sep 06 2018 a(n) = (11/2)*(n mod 2) + 15*n/2 - 2 for n > 0. - Mikk Heidemaa, Sep 08 2018 f(n) = 15*n - ((13*n + 17) mod 26) for n > 0 yields odd terms. - Mikk Heidemaa, Oct 28 2019 a(n) = 11*ceiling(1/2*n) + 2*n - 2 for n > 0. - Mikk Heidemaa, Nov 04 2019 MAPLE P:=proc(n) if n mod 15=11 or n mod 15=13 then n; fi; end: seq(P(i), i=1..500); # Paolo P. Lava, Dec 11 2017 MATHEMATICA ParallelMap[11 * Ceiling[#/2] + 2 * # - 2 &, Range@ 10^3] CoefficientList[ Series[(2x^2 + 2x + 11)/((1 + x) (x - 1)^2), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, -1}, {11, 13, 26}, 60] (* Robert G. Wilson v, Jan 09 2018 *) Select[Range[500], MemberQ[{11, 13}, Mod[#, 15]] &] (* Vincenzo Librandi, Sep 06 2018 *) 11/2 * Mod[#, 2] + 15 * #/2 - 2 &/@ Range@ 500 (* Mikk Heidemaa, Sep 08 2018 *) PROG (PARI) Vec(x*(11 + 2*x + 2*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Dec 07 2017 (PARI) a(n) = if(n%2, (15*n+7)/2, (15*n-4)/2); \\ Altug Alkan, Sep 06 2018 (PARI) a(n) = [11, -2][(n - 1)%2 + 1] + 15*(n \ 2) \\ David A. Corneth, Sep 06 2018 (MAGMA) [n: n in [1..500] | n mod 15 in [11, 13]]; // Vincenzo Librandi, Sep 06 2018 CROSSREFS Cf. A132238, A132241. Sequence in context: A275598 A090433 A022325 * A153055 A146915 A067786 Adjacent sequences:  A295337 A295338 A295339 * A295341 A295342 A295343 KEYWORD nonn,easy AUTHOR Mikk Heidemaa, Nov 20 2017 EXTENSIONS Name simplified by David A. Corneth, Sep 06 2018 STATUS approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)