cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A132247 Twin primes congruent to {1, 11, 13, 17, 19, 29} mod 30.

Original entry on oeis.org

11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109, 137, 139, 149, 151, 179, 181, 191, 193, 197, 199, 227, 229, 239, 241, 269, 271, 281, 283, 311, 313, 347, 349, 419, 421, 431, 433, 461, 463, 521, 523, 569, 571, 599, 601, 617, 619, 641, 643
Offset: 1

Views

Author

Omar E. Pol, Aug 18 2007

Keywords

Comments

Twin primes that are greater than 7. - Omar E. Pol, Oct 31 2013

Links

Crossrefs

Cf. A001097, A039949, A132230, A132232-A132234, A132236, A132238-A132246, A132248-A132259.

Formula

a(n) = A001097(n+3). - Michel Marcus, Nov 03 2013

A229947 Primes congruent to {1, 11, 13, 17, 19, 29} mod 30.

Original entry on oeis.org

11, 13, 17, 19, 29, 31, 41, 43, 47, 59, 61, 71, 73, 79, 89, 101, 103, 107, 109, 131, 137, 139, 149, 151, 163, 167, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 257, 269, 271, 281, 283, 311, 313, 317, 331, 347, 349, 359, 373, 379, 389
Offset: 1

Views

Author

Omar E. Pol, Oct 27 2013

Keywords

Comments

For twin primes congruent to {1, 11, 13, 17, 19, 29} mod 30 see A132247.
Complement of A132237, primes congruent to 7 or 23 (mod 30), in the set of primes > 5. - M. F. Hasler, Nov 02 2013

Links

Crossrefs

Cf. A000040, A001097, A039949, A132230, A132232-A132234, A132236, A132238-A132259, A230462.

Programs

  • Magma
    [p: p in PrimesUpTo(500) | p mod 30 in {1,11,13,17, 19,29} ]; // Vincenzo Librandi, Apr 05 2015
  • Mathematica
    Select[Flatten[Table[30n + {1, 11, 13, 17, 19, 29}, {n, 0, 11}]], PrimeQ] (* Alonso del Arte, Nov 01 2013 *)
Select[Prime@Range[100], MemberQ[{1, 11, 13, 17, 19, 29}, Mod[#, 30]] &] (* Vincenzo Librandi, Apr 05 2015 *)
  • PARI
    is(n)=isprime(n) && setsearch([1,11,13,17,19,29], n%30) \\ Charles R Greathouse IV, Mar 08 2015

Formula

a(n) ~ 4/3 n log n. - Charles R Greathouse IV, Mar 08 2015

A295340 Numbers congruent to 11 or 13 mod 15.

Original entry on oeis.org

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

Views

Author

Mikk Heidemaa, Nov 20 2017

Keywords

Comments

Includes every prime and twin prime (as pairs of consecutive primes) congruent to 11 or 13 mod 30.

Links

Crossrefs

Cf. A132238 (subsequence of primes), A132241 (subsequence of twin primes).

Programs

  • Magma
    [n: n in [1..500] | n mod 15 in [11, 13]]; // Vincenzo Librandi, Sep 06 2018
  • 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 *)
  • 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

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

Extensions

Name simplified by David A. Corneth, Sep 06 2018
Showing 1-3 of 3 results.

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