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.

A274903 Largest prime factor of 4^n + 1.

Original entry on oeis.org

2, 5, 17, 13, 257, 41, 241, 113, 65537, 109, 61681, 2113, 673, 1613, 15790321, 1321, 6700417, 26317, 38737, 525313, 4278255361, 14449, 2931542417, 30269, 22253377, 268501, 308761441, 279073, 54410972897, 536903681, 4562284561, 384773, 67280421310721
Offset: 0

Views

Author

Vincenzo Librandi, Jul 11 2016

Keywords

Examples

			4^3 + 1 = 65 = 5*13, so a(3) = 13.

Links

Crossrefs

Cf. largest prime factor of k^n+1: A002587 (k=2), A074476 (k=3), this sequence (k=4), A074478 (k=5), A274904 (k=6), A227575 (k=7), A274905 (k=8), A002592 (k=9), A003021 (k=10), A062308 (k=11).
Cf. A006530, A052539.

Programs

  • Magma
    [Maximum(PrimeDivisors(4^n+1)): n in [0..35]];
  • Mathematica
    Table[FactorInteger[4^n + 1][[-1, 1]], {n, 0, 30}]
  • PARI
    a(n)=my(f=factor(4^n+1)[,1]); f[#f] \\ Charles R Greathouse IV, Jul 12 2016

Formula

a(n) = A006530(A052539(n)). - Michel Marcus, Jul 11 2016
a(2n) = A002590(n). a(2n+1) = A229747(n). - R. J. Mathar, Feb 28 2018
a(n) = A002587(2*n). - Amiram Eldar, Feb 01 2020

Extensions

Terms to a(100) in b-file from Vincenzo Librandi, Jul 12 2016
a(101)-a(531) in b-file from Amiram Eldar, Feb 01 2020
a(532)-a(583) in b-file from Max Alekseyev, Apr 25 2022, Mar 15 2025

A229767 Largest prime factor of 2^(2*n+1)-2^(n+1)+1.

Original entry on oeis.org

5, 5, 113, 37, 397, 1613, 61, 953, 457, 14449, 30269, 8101, 246241, 107367629, 384773, 312709, 47392381, 184481113, 1249, 12112549, 1759217765581, 54001, 140737471578113, 4981857697937, 26317, 1801439824104653, 415878438361, 525313, 174877, 368140581013
Offset: 1

Views

Author

Colin Barker, Sep 29 2013

Keywords

Comments

2^(2*n+1)-2^(n+1)+1 is a factor of 4^(2*n+1)+1.

Examples

			For n=5, 2^(2*n+1)-2^(n+1)+1 = 1985 = 5*397, so a(5)=397.

Links

Crossrefs

Cf. A092440, A207262, A229747, A229768.

Programs

  • PARI
    a(n) = {f=factor(2^(2*n+1)-2^(n+1)+1); f[matsize(f)[1],1]}

A229768 Largest prime factor of 2^(2*n+1)+2^(n+1)+1.

Original entry on oeis.org

13, 41, 29, 109, 2113, 157, 1321, 26317, 525313, 1429, 1657, 268501, 279073, 536903681, 49477, 4327489, 7416361, 231769777, 21841, 43249589, 500177, 29247661, 7484047069, 19707683773, 1326700741, 586477649, 3630105520141, 275415303169, 104399276341
Offset: 1

Views

Author

Colin Barker, Sep 29 2013

Keywords

Comments

2^(2*n+1)+2^(n+1)+1 is a factor of 4^(2*n+1)+1.

Examples

			For n=10, 2^(2*n+1)+2^(n+1)+1 = 2099201 = 13*113*1429, so a(10)=1429.

Links

Crossrefs

Cf. A085601, A207262, A229747, A229767.

Programs

  • Mathematica
    Table[FactorInteger[2^(2n+1)+2^(n+1)+1][[-1,1]],{n,30}] (* Harvey P. Dale, Nov 03 2017 *)
  • PARI
    a(n) = {f=factor(2^(2*n+1)+2^(n+1)+1); f[matsize(f)[1],1]}
Showing 1-3 of 3 results.

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

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