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.

A242083 a(n) = 3^p - 2^p - 1, where p is prime(n).

Original entry on oeis.org

4, 18, 210, 2058, 175098, 1586130, 129009090, 1161737178, 94134790218, 68629840493970, 617671248800298, 450283768452043890, 36472994178147530850, 328256958598444055418, 26588814218220014932458, 19383245658672820642055730
Offset: 1

Views

Author

Vincenzo Librandi, May 04 2014

Keywords

Comments

For p>3, all terms are divisible by 42.

Crossrefs

Programs

  • Magma
    [3^p-2^p-1: p in PrimesUpTo(60)];
    
  • Mathematica
    Table[(3^Prime[n] - 2^Prime[n] - 1), {n, 1, 30}]
    3^#-2^#-1&/@Prime[Range[20]] (* Harvey P. Dale, Aug 05 2016 *)
  • PARI
    a(n) = my(p = prime(n)); 3^p-2^p-1; \\ Michel Marcus, May 05 2014
    
  • Sage
    [3^p-2^p-1 for p in primes(60)] # Bruno Berselli, May 12 2014

Formula

a(n) = abs(A083321(A000040(n))). - Michel Marcus, May 05 2014

A242084 5^p - 4^p - 1, where p is prime.

Original entry on oeis.org

8, 60, 2100, 61740, 44633820, 1153594260, 745759583940, 18798608421180, 11850560210900460, 185976284546943991380, 4652001187058965190220, 72740686675902780452348340, 45469899385367953379053128420
Offset: 1

Views

Author

Vincenzo Librandi, May 04 2014

Keywords

Comments

For p>3 all terms are divisible by 21.

Crossrefs

Cf. A204768.

Programs

  • Magma
    [5^p-4^p-1: p in PrimesUpTo(60)];
    
  • Mathematica
    Table[5^Prime[n] - 4^Prime[n] - 1, {n, 1, 60}]
  • PARI
    a(n) = my(p = prime(n)); 5^p - 4^p - 1; \\ Michel Marcus, May 05 2014

Formula

a(n) = A054401(A000040(n)). - Michel Marcus, May 05 2014

A209901 7^p - 6^p - 2 with p = prime(n).

Original entry on oeis.org

11, 125, 9029, 543605, 1614529685, 83828316389, 215703854542469, 10789535445362645, 26579017117027313525, 3183060102526390833854309, 156448938516521406467644085, 18500229372226631089176131976869, 44487435359130133495783012898708549
Offset: 1

Views

Author

Jonathan Vos Post, Mar 14 2012

Keywords

Comments

After 11 and 9029, there are no prime values of a(n) through 7^109 - 6^109 - 2.

Examples

			543605 is in the sequence because 543605 = 7^7 - 6^7 - 2, and 7 is prime.
		

Crossrefs

Programs

  • Mathematica
    Table[7^p - 6^p - 2, {p, Prime[Range[20]]}] (* T. D. Noe, Mar 15 2012 *)
  • PARI
    forprime(p=2,100,print1(7^p-6^p-2", ")) \\ Charles R Greathouse IV, Mar 15 2012

Formula

a(n) = A016169(A000040(n)) - 2 = A204768(n) - 1 = A000420(A000040(n)) - A000400(A000040(n)) - 2.
Showing 1-3 of 3 results.