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.

A051156 a(n) = (2^p^2 - 1)/(2^p - 1) where p is the n-th prime.

Original entry on oeis.org

5, 73, 1082401, 4432676798593, 1298708349570020393652962442872833, 91355004067076339167413824240109498970069278721, 7588608256743087977590500540116743445925584618982806531428980886590618779326218241
Offset: 1

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Author

Keywords

Comments

Note that a(n) = Phi(p,2^p) or a(n) = Phi(p^2,2), where Phi(m,x) is the m-th cyclotomic polynomial and p is the n-th prime. - Thomas Ordowski, Feb 18 2014

Crossrefs

Programs

  • Mathematica
    Table[Cyclotomic[Prime[n]^2, 2], {n, 7}] (* Arkadiusz Wesolowski, May 13 2012 *)
    Table[(2^Prime[n]^2-1)/(2^Prime[n]-1),{n,10}] (* Harvey P. Dale, Apr 06 2019 *)

Formula

a(n) = A070526(prime(n)), a(n) = A019320(prime(n)^2). - Thomas Ordowski, Feb 18 2014

A128889 a(n) = (2^(n^2) - 1)/(2^n - 1).

Original entry on oeis.org

1, 5, 73, 4369, 1082401, 1090785345, 4432676798593, 72340172838076673, 4731607904558235517441, 1239150146850664126585242625, 1298708349570020393652962442872833, 5445847423328601499764522166702896582657, 91355004067076339167413824240109498970069278721
Offset: 1

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Author

Leroy Quet, Apr 19 2007

Keywords

Comments

a(n) is prime for n in A156585. Conjecture: gpf(a(n)) = gpf(Phi(n,2^n)), where Phi(n,2^n) = A070526(n). - Thomas Ordowski, Feb 16 2014
The conjecture fails at n = 26, where 3340762283952395329506327023033 > 215656329382891550920192462661. Next counterexample for n = 30, but no odd counterexamples found so far. - Charles R Greathouse IV, Feb 17 2014

Crossrefs

Programs

  • Maple
    a:=n->(2^(n^2)-1)/(2^n-1): seq(a(n),n=1..13);
  • Mathematica
    f[n_] := (2^(n^2) - 1)/(2^n - 1); Array[f, 12]
    F[n_] := Plus @@ Table[2^((n - i)*n), {i, 1, n}] (* Enrique Pérez Herrero, Feb 23 2009 *)
    Table[(2^(n^2) - 1)/(2^n - 1), {n, 1, 20}] (* Vincenzo Librandi, Feb 18 2014 *)
  • PARI
    a(n)=(2^n^2-1)/(2^n-1) \\ Charles R Greathouse IV, Feb 17 2014

Formula

a(n) = Sum_{k=1..n} 2^((n-k)*n). - Enrique Pérez Herrero, Feb 23 2009

Extensions

More terms from Robert G. Wilson v and Emeric Deutsch, Apr 22 2007

A070527 Numbers k such that cyclotomic(k, 2^k) is a prime number.

Original entry on oeis.org

2, 3, 4, 7, 40, 59, 140
Offset: 1

Views

Author

Labos Elemer, May 02 2002

Keywords

Comments

No other terms below 300. - Max Alekseyev, May 29 2009
No other terms below 760. - Lucas A. Brown, Dec 16 2020

Examples

			4 is a term because cyclotomic(4,16) = 1 + 16^2 = 257 is prime.
		

Crossrefs

Programs

  • Mathematica
    Do[s=Cyclotomic[n, 2^n]; If[PrimeQ[s], Print[n]], {n, 1, 1000}]
    Select[Range[150],PrimeQ[Cyclotomic[#,2^#]]&] (* Harvey P. Dale, Aug 12 2023 *)
  • PARI
    isok(k) = isprime(polcyclo(k, 2^k)); \\ Michel Marcus, Dec 17 2020

Extensions

One more term from Max Alekseyev, May 29 2009
Showing 1-3 of 3 results.