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.

Previous Showing 11-15 of 15 results.

A062308 Largest prime factor of 11^n+1 (A034524).

Original entry on oeis.org

2, 3, 61, 37, 7321, 13421, 1117, 1623931, 6304673, 590077, 212601841, 58367, 20113, 59583967, 55527473, 7537711, 447600088289, 2218331, 3138426605161, 1390636259, 1120648576818041, 3421169496361, 2649263870814793
Offset: 0

Views

Author

Jason Earls, Jul 12 2001

Keywords

Crossrefs

Cf. similar sequences listed in A274903.

Programs

  • Magma
    [Maximum(PrimeDivisors(11^n+1)): n in [0..40]]; // Vincenzo Librandi, Jul 12 2016
  • Mathematica
    Table[FactorInteger[11^n + 1][[-1, 1]], {n, 0, 20}] (* Vincenzo Librandi, Jul 12 2016 *)
  • PARI
    for(n=0,22,print(factor(11^n+1)))
    
  • PARI
    { for (n=0, 80, f=factor(11^n + 1)~; write("b062308.txt", n, " ", f[1, length(f)]) ) } \\ Harry J. Smith, Aug 04 2009
    

Formula

a(n) = A006530(A034524(n)). - Vincenzo Librandi, Jul 12 2016

Extensions

Terms to a(80) in b-file from Harry J. Smith, Jun 01 2010
a(81)-a(301) in b-file from Amiram Eldar, Feb 08 2020
a(302)-a(325) in b-file from Max Alekseyev, Apr 25 2022, Oct 11 2023

A366720 Largest prime factor of 12^n+1.

Original entry on oeis.org

2, 13, 29, 19, 233, 19141, 20593, 13063, 260753, 1801, 85403261, 57154490053, 2227777, 222379, 13156924369, 35671, 1200913648289, 66900193189411, 122138321401, 905265296671, 67657441, 1885339, 68368660537, 49489630860836437, 592734049, 438472201
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Crossrefs

Programs

  • Mathematica
    Table[FactorInteger[12^n + 1][[-1, 1]], {n, 0, 20}]

Formula

a(n) = A006530(A178248(n)). - Paul F. Marrero Romero, Dec 07 2023

A274904 Largest prime factor of 6^n + 1.

Original entry on oeis.org

2, 7, 37, 31, 1297, 101, 97, 197, 98801, 46441, 6781, 51828151, 1678321, 37571, 5030761, 1950271, 4709377, 12690943, 55117, 48713705333, 68754507401, 2527867231, 863017, 990000731, 473896897, 3655688315536801, 6291946695217, 883383463, 81035189089
Offset: 0

Views

Author

Vincenzo Librandi, Jul 11 2016

Keywords

Examples

			6^3 + 1 = 217 = 7*31, so a(3) = 31.
		

Crossrefs

Cf. similar sequences listed in A274903.

Programs

  • Magma
    [Maximum(PrimeDivisors(6^n+1)): n in [0..40]];
  • Mathematica
    Table[FactorInteger[6^n + 1][[-1, 1]], {n, 0, 40}]

Formula

a(n) = A006530(A062394(n)). - Michel Marcus, Jul 11 2016

Extensions

Terms to a(100) in b-file from Vincenzo Librandi, Jul 12 2016
a(101)-a(408) in b-file from Amiram Eldar, Feb 02 2020
a(409)-a(430) in b-file from Max Alekseyev, Apr 25 2022, Apr 15 2025

A229747 Largest prime factor of 4^(2*n+1)+1.

Original entry on oeis.org

5, 13, 41, 113, 109, 2113, 1613, 1321, 26317, 525313, 14449, 30269, 268501, 279073, 536903681, 384773, 4327489, 47392381, 231769777, 21841, 43249589, 1759217765581, 29247661, 140737471578113, 4981857697937, 1326700741, 1801439824104653, 3630105520141
Offset: 0

Views

Author

Colin Barker, Sep 28 2013

Keywords

Comments

4^(2*n+1)+1 = 2^(2*(2*n+1))+1 = (2^(2*n+1)-2^(n+1)+1) * (2^(2*n+1)+2^(n+1)+1).
For all n, the smallest prime factor of 4^(2*n+1)+1 is 5.
Therefore, the present sequence also gives the largest prime factor of (4^(2*n+1)+1)/5 = A299960(n), for all n > 0. See A299959 for the smallest prime factor of this. - M. F. Hasler, Feb 27 2018

Examples

			For n=7, 4^(2*n+1)+1 = 1073741825 = 5*5*13*41*61*1321. So a(7)=1321.
		

Crossrefs

Cf. A207262. Bisection of A274903.

Programs

  • Mathematica
    Table[FactorInteger[4^(2n+1)+1][[-1,1]],{n,0,30}] (* Harvey P. Dale, Mar 10 2018 *)
  • PARI
    a(n) = {
      f=factor(2^(2*n+1)-2^(n+1)+1);
      g=factor(2^(2*n+1)+2^(n+1)+1);
      max(f[matsize(f)[1],1], g[matsize(g)[1],1])
    }

Formula

a(n) = A006530(A052539(2n+1)) = A006530(A207262(n+1)), and for n > 1, a(n) = A006530(A299960(n)) = A006530(A052539(2n+1)/5). \\ M. F. Hasler, Feb 27 2018
a(n) = max(A229767(n), A229768(n)), for n >= 1. - Daniel Suteu, Jun 08 2022

A324941 Largest prime factor of 17^n + 1.

Original entry on oeis.org

2, 3, 29, 13, 41761, 101, 83233, 22796593, 184417, 5653, 63541, 87415373, 72337, 2001793, 100688449, 238212511, 52548582913, 45957792327018709121, 382069, 20352763, 1186844128302568601, 88109799136087, 6901823633, 1109309383381084655697725873, 48661191868691111041
Offset: 0

Views

Author

Vincenzo Librandi, Apr 05 2019

Keywords

Crossrefs

Programs

  • Magma
    [Maximum(PrimeDivisors(17^n + 1)): n in [0..40]];
    
  • Mathematica
    Table[FactorInteger[17^n + 1] [[-1,1]], {n, 0, 30}]
  • PARI
    a(n) = vecmax(factor(17^n+1)[, 1]); \\ Jinyuan Wang, Apr 05 2019

Formula

a(n) = A006530(A224384(n)).
Previous Showing 11-15 of 15 results.