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.

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)

A229855 a(n) = 384*n + 257.

Original entry on oeis.org

257, 641, 1025, 1409, 1793, 2177, 2561, 2945, 3329, 3713, 4097, 4481, 4865, 5249, 5633, 6017, 6401, 6785, 7169, 7553, 7937, 8321, 8705, 9089, 9473, 9857, 10241, 10625, 11009, 11393, 11777, 12161, 12545, 12929, 13313, 13697, 14081, 14465, 14849, 15233, 15617, 16001
Offset: 0

Views

Author

Arkadiusz Wesolowski, Oct 01 2013

Keywords

Comments

Every composite Fermat number has at least two divisors of the form 384*n + 257, n > 0.

Links

Crossrefs

Cf. A000215, A016789, A094358, A229853, A229854, A229856.

Programs

  • Magma
    [384*n+257 : n in [0..40]];
  • Maple
    seq(384*n+257, n=0..40);
  • Mathematica
    Table[384*n + 257, {n, 0, 40}]
  • PARI
    for(n=0, 40, print1(384*n+257, ", "));

Formula

G.f.: (257 + 127*x)/(1 - x)^2.
a(n) = 128*A016789(n) + 1.
From Elmo R. Oliveira, Dec 08 2024: (Start)
E.g.f.: exp(x)*(257 + 384*x).
a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)

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]
Showing 1-3 of 3 results.

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

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