login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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