A295340 Numbers congruent to 11 or 13 mod 15.

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

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) = 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

E.g.f.: 2 + ((30*x + 3)*exp(x) - 11*exp(-x))/4. - David Lovler, Sep 08 2022

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 (subsequence of primes), A132241 (subsequence of twin primes).

Sequence in context: A090433 A374059 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