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 1-4 of 4 results.

A229853 a(n) = 384*n + 1.

Original entry on oeis.org

1, 385, 769, 1153, 1537, 1921, 2305, 2689, 3073, 3457, 3841, 4225, 4609, 4993, 5377, 5761, 6145, 6529, 6913, 7297, 7681, 8065, 8449, 8833, 9217, 9601, 9985, 10369, 10753, 11137, 11521, 11905, 12289, 12673, 13057, 13441, 13825, 14209, 14593, 14977, 15361, 15745
Offset: 0

Views

Author

Arkadiusz Wesolowski, Oct 01 2013

Keywords

Comments

Every composite Fermat number has a divisor of the form 384*n + 1, n > 0.

Links

Crossrefs

Cf. A000215, A094358, A229854, A229855, A229856.

Programs

  • Magma
    [384*n+1 : n in [0..40]];
  • Maple
    seq(384*n+1, n=0..40);
  • Mathematica
    Table[384*n + 1, {n, 0, 40}]
  • PARI
    for(n=0, 40, print1(384*n+1, ", "));

Formula

G.f.: (1 + 383*x)/(1 - x)^2.
From Elmo R. Oliveira, Apr 04 2025: (Start)
E.g.f.: exp(x)*(1 + 384*x).
a(n) = 2*a(n-1) - a(n-2). (End)

A229856 Primes of the form 384*k + 257.

Original entry on oeis.org

257, 641, 1409, 3329, 4481, 7937, 9473, 9857, 11393, 11777, 12161, 13313, 13697, 14081, 15233, 16001, 17921, 19073, 19457, 19841, 21377, 23297, 25601, 28289, 30593, 30977, 35201, 35969, 36353, 37889, 38273, 39041, 40193, 40577, 40961, 41729, 43649, 44417
Offset: 1

Views

Author

Arkadiusz Wesolowski, Oct 01 2013

Keywords

Comments

Every Fermat number greater than 257 has a prime factor of the form 384*k + 257, k > 0.

Links

Crossrefs

Subsequence of A107181 (primes of the form 8x^2+9y^2).
Cf. A000215, A023394, A094358, A229853, A229855, A229856.

Programs

  • Magma
    [384*n+257 : n in [0..115] | IsPrime(384*n+257)];
  • Mathematica
    Select[Table[384*n + 257, {n, 0, 115}], PrimeQ]

A229854 Primes of the form 384*k + 1.

Original entry on oeis.org

769, 1153, 2689, 3457, 4993, 6529, 7297, 7681, 9601, 10369, 10753, 12289, 13441, 14593, 15361, 18049, 18433, 20353, 21121, 22273, 23041, 26113, 26497, 26881, 29569, 31489, 31873, 32257, 33409, 36097, 37633, 39937, 43777, 45697, 49537, 49921, 52609, 53377
Offset: 1

Views

Author

Arkadiusz Wesolowski, Oct 01 2013

Keywords

Comments

Not every composite Fermat number has a prime factor of the form 384*k + 1.

Links

Crossrefs

Subsequence of A002476 (primes of form 6m + 1).
Cf. A000215, A023394, A094358, A229850, A229853, A229855, A229856.

Programs

  • Magma
    [384*n+1 : n in [1..139] | IsPrime(384*n+1)];
  • Mathematica
    Select[Table[384*n + 1, {n, 139}], PrimeQ]

A242215 a(n) = 18*n + 5.

Original entry on oeis.org

5, 23, 41, 59, 77, 95, 113, 131, 149, 167, 185, 203, 221, 239, 257, 275, 293, 311, 329, 347, 365, 383, 401, 419, 437, 455, 473, 491, 509, 527, 545, 563, 581, 599, 617, 635, 653, 671, 689, 707, 725, 743, 761, 779, 797, 815, 833, 851, 869, 887, 905, 923, 941, 959
Offset: 0

Views

Author

Arkadiusz Wesolowski, May 07 2014

Keywords

Comments

Conjecture: there are infinitely many composite Fermat numbers such that no one of them has a divisor that belongs to this sequence.

Links

Crossrefs

Supersequence of A061240.
Cf. A229855.

Programs

  • Magma
    [18*n+5: n in [0..53]];
  • Maple
    seq(18*n+5, n=0..53);
  • Mathematica
    Table[18*n + 5, {n, 0, 53}]
LinearRecurrence[{2,-1},{5,23},60] (* Harvey P. Dale, Aug 25 2017 *)
  • PARI
    for(n=0, 53, print1(18*n+5, ", "));

Formula

G.f.: (5 + 13*x)/(1 - x)^2.
From Elmo R. Oliveira, Dec 08 2024: (Start)
E.g.f.: exp(x)*(5 + 18*x).
a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)
Showing 1-4 of 4 results.

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