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 1-6 of 6 results.

A135659 a(n) = 24*n + 7.

Original entry on oeis.org

7, 31, 55, 79, 103, 127, 151, 175, 199, 223, 247, 271, 295, 319, 343, 367, 391, 415, 439, 463, 487, 511, 535, 559, 583, 607, 631, 655, 679, 703, 727, 751, 775, 799, 823, 847, 871, 895, 919, 943, 967, 991, 1015, 1039, 1063, 1087, 1111, 1135, 1159, 1183, 1207
Offset: 0

Views

Author

Artur Jasinski, Nov 25 2007

Keywords

Comments

Conjecture: All Mersenne Primes (A000668) > 3 are in this sequence.

Links

Crossrefs

Cf. A107006, A124477, A135657, A135982.

Programs

  • Mathematica
    Table[24n + 7, {n, 0, 100}]
LinearRecurrence[{2,-1},{7,31},60] (* Harvey P. Dale, Jul 14 2013 *)

Formula

From Colin Barker, Apr 02 2012: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (7+17*x)/(1-x)^2. (End)
E.g.f.: (7 + 24*x)*exp(x). - G. C. Greubel, Oct 25 2016

Extensions

Offset changed to 0 by Omar E. Pol, Oct 25 2016

A135982 a(n) = 2^(24n+7)-1.

Original entry on oeis.org

127, 2147483647, 36028797018963967, 604462909807314587353087, 10141204801825835211973625643007, 170141183460469231731687303715884105727
Offset: 0

Views

Author

Artur Jasinski, Dec 09 2007

Keywords

Links

Crossrefs

Cf. A107006, A124477, A135657.

Programs

Formula

a(n) = 2^A135659(n) - 1.
G.f.: ( 127+16777088*x ) / ( (16777216*x-1)*(x-1) ). - R. J. Mathar, Apr 02 2012

A135983 a(n)=2^A107006(n)-1.

Original entry on oeis.org

127, 2147483647, 604462909807314587353087, 10141204801825835211973625643007, 170141183460469231731687303715884105727, 2854495385411919762116571938898990272765493247
Offset: 1

Views

Author

Artur Jasinski, Dec 09 2007

Keywords

Comments

A107006(n) are successive primes of the form 24n+7.

Crossrefs

Cf. A107006, A124477, A135657, A135982.

Programs

  • Mathematica
    p = Select[24*Range[0, 20] + 7, PrimeQ]; 2^p - 1

A135984 a(n) = 24(prime(n))+7.

Original entry on oeis.org

55, 79, 127, 175, 271, 319, 415, 463, 559, 703, 751, 895, 991, 1039, 1135, 1279, 1423, 1471, 1615, 1711, 1759, 1903, 1999, 2143, 2335, 2431, 2479, 2575, 2623, 2719, 3055, 3151, 3295, 3343, 3583, 3631, 3775, 3919, 4015, 4159, 4303, 4351, 4591, 4639, 4735
Offset: 1

Views

Author

Artur Jasinski, Dec 09 2007

Keywords

Crossrefs

Cf. A107006, A124477, A135657, A135982, A135983.

Programs

  • Mathematica
    Table[24*Prime[n] + 7, {n, 1, 100}]

A135985 Prime numbers of the form 24*p + 7 where p is prime.

Original entry on oeis.org

79, 127, 271, 463, 751, 991, 1039, 1279, 1423, 1471, 1759, 1999, 2143, 2719, 3343, 3583, 3631, 3919, 4159, 4591, 4639, 4783, 5503, 5743, 5791, 7039, 7951, 8623, 9103, 9199, 9343, 9631, 10111, 10399, 10639, 11071, 11119, 11503, 12511
Offset: 1

Views

Author

Artur Jasinski, Dec 09 2007

Keywords

Links

Crossrefs

Cf. A107006, A124477, A135657, A135982, A135983, A135984.

Programs

  • Maple
    select(t -> isprime(t) and isprime((t-7)/24), [seq(p,p=7..20000,24)]); # Robert Israel, Oct 16 2018
  • Mathematica
    a = {}; Do[If[PrimeQ[24(Prime[n]) + 7], AppendTo[a, 24(Prime[n]) + 7]], {n, 1, 100}]; a

A135658 Nonprimes of the form 4x^2-4xy+7y^2.

Original entry on oeis.org

4, 15, 16, 24, 28, 36, 40, 55, 60, 63, 64, 87, 88, 96, 100, 112, 124, 132, 135, 144, 159, 160, 168, 175, 196, 216, 220, 231, 232, 240, 247
Offset: 1

Views

Author

Artur Jasinski, Nov 25 2007

Keywords

Comments

Because 4x^2-4*x*y+7*y^2 = (2*x-y)^2+6*y^2, this is a subsequence of A002481. - R. J. Mathar, Jan 18 2021

Crossrefs

Cf. A107006, A124477, A135657.

Programs

  • Mathematica
    Do[Do[w = 4x^2 - 4x y + 7y^2; If[w > 0, If[PrimeQ[w],[null], AppendTo[a, w]]], {x, 0, 100}], {y, 0, 100}]; Union[a]
Showing 1-6 of 6 results.

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