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.

A230809 Primes p of the form 60*n + 59 such that 2*p + 1 is also prime.

Original entry on oeis.org

179, 239, 359, 419, 659, 719, 1019, 1439, 1499, 1559, 2039, 2339, 2399, 2459, 2699, 2819, 2939, 3299, 3359, 3539, 3779, 4019, 4919, 5039, 5279, 5399, 5639, 6899, 7079, 9059, 9419, 9479, 9539, 10799, 11519, 11579, 11699, 11939, 12119, 12899, 12959, 13619
Offset: 1

Views

Author

Arkadiusz Wesolowski, Oct 30 2013

Keywords

Comments

Primes p such that 2*p + 1 divides Lucas(p) and Mersenne(p).

Examples

			179 is in the sequence since it is prime and 359 is a factor of both Lucas(179) and Mersenne(179) = 2^179 - 1.

Links

Crossrefs

Subsequence of A142799, of A215850, and of A239548. Cf. A000032, A001348, A002515.

Programs

  • Magma
    [p : p in [59..13619 by 60] | IsPrime(p) and IsPrime(2*p+1)];
  • PARI
    forstep(p=59, 13619, 60, if(isprime(p)&&isprime(2*p+1), print1(p, ", ")));

Formula

A005384 INTERSECT A142799.
A002515 INTERSECT A215850.

A263769 Smallest prime q such that q == -1 (mod prime(n)-1).

Original entry on oeis.org

2, 3, 3, 5, 19, 11, 31, 17, 43, 83, 29, 71, 79, 41, 137, 103, 173, 59, 131, 139, 71, 233, 163, 263, 191, 199, 101, 211, 107, 223, 251, 389, 271, 137, 443, 149, 311, 647, 331, 859, 1423, 179, 379, 191, 587, 197, 419, 443
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Oct 25 2015

Keywords

Comments

a(n): A000040(1), A065091(1), A002145(1), A007528(1), A030433(1), A068231(1), A127576(1), A061242(1), A141857(1), A141976(1), A132236(1), A142111(1), A142198(1), A141898(1), A141926(1), A142531(1), A142004(1), A142799(1), A142068(1), A142099(1), ...
Smallest prime q such that (prime(n)^2 + q*prime(n))/(prime(n) + 1) is an integer.

Examples

			a(4) = 5 because 5 == -1 (mod prime(4)-1) and is prime.

Links

Crossrefs

Cf. A263730, A263770.
Cf. A000040, A065091, A002145, A007528, A030433, A068231, A127576, A061242, A141857, A141976, A132236, A142111, A142198, A141898, A141926, A142531, A142004, A142799, A142068, A142099.

Programs

  • Maple
    for n from 1 to 100 do
  k:= ithprime(n)-1;
  q:= 2;
  while (1 + q) mod k <> 0 do
    q:= nextprime(q)
  od;
  A[n]:= q;
od:
seq(A[i],i=1..1000); # Robert Israel, Oct 26 2015
  • Mathematica
    Table[q = 2; z = Prime@ n - 1; While[Mod[q, z] != z - 1, q = NextPrime@ q]; q, {n, 59}] (* Michael De Vlieger, Oct 26 2015 *)

Extensions

Corrected and edited by Robert Israel, Oct 26 2015,

A142786 Primes congruent to 7 mod 60.

Original entry on oeis.org

7, 67, 127, 307, 367, 487, 547, 607, 727, 787, 907, 967, 1087, 1327, 1447, 1567, 1627, 1747, 1867, 1987, 2287, 2347, 2467, 2647, 2707, 2767, 2887, 3067, 3187, 3307, 3547, 3607, 3727, 3847, 3907, 3967, 4027, 4327, 4447, 4507, 4567, 4987, 5107, 5167, 5227
Offset: 1

Views

Author

N. J. A. Sloane, Jul 11 2008

Keywords

Comments

Comment from Joshua S.M. Weiner, Oct 12 2012 (Start)
Intersection of A068229 and A141882. Subsequence of A132231.
Congruence classes of primes mod 60: A088955 (1), (this sequence 7), A117047 (11), A142787 (13), A142788 (17), A142789 (19), A142790 (23), A142791 (29), A142792 (31), A142793 (37), A142794 (41), A142795 (43), A142796 (47), A142797 (49), A142798 (53), A142799 (59). (End)

Links

Crossrefs

Cf. A000040, A142322.

Programs

  • Magma
    [p: p in PrimesUpTo(6000) | p mod 60 eq 7 ]; // Vincenzo Librandi, Sep 04 2012
  • Mathematica
    Select[Prime[Range[1000]], Mod[#, 60] == 7 &] (* T. D. Noe, Oct 12 2012 *)
Select[Range[7,5300,60],PrimeQ] (* Harvey P. Dale, Nov 21 2018 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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