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.

A090528 Primes arising in A090527.

Original entry on oeis.org

2, 13, 23, 107, 4241, 6011, 212369, 2600137, 769230769, 16783039447, 49260223471, 43267872370321, 156507138388141, 10680338789777057, 348051774975651917, 1529094753948866477, 199727959773078870941, 32433109109185468674163
Offset: 1

Views

Author

Amarnath Murthy, Dec 07 2003

Keywords

Comments

Conjecture: No term is zero.

Crossrefs

Cf. A090525, A090526, A090527.

Programs

  • Mathematica
    Do[p = n^n; i = 1; While[ !ProvablePrimeQ[Floor[p/Prime[i]]], i++ ]; Print[Floor[p/Prime[i]]], {n, 2, 50}] (* Ryan Propper, Aug 02 2005 *)

Extensions

More terms from Ryan Propper, Aug 02 2005

A090525 Least number k such that floor((n^n)/k) is prime, or 0 if no such number exists.

Original entry on oeis.org

2, 2, 11, 9, 11, 20, 10, 42, 13, 16, 57, 7, 35, 41, 53, 35, 171, 18, 141, 45, 19, 55, 212, 236, 94, 265, 13, 76, 26, 9, 13, 21, 160, 21, 21, 24, 378, 100, 66, 52, 75, 54, 214, 6, 678, 193, 137, 123, 138, 59, 605, 87, 165, 109, 417, 403, 100, 57, 778, 719, 79, 12, 83, 450
Offset: 2

Views

Author

Amarnath Murthy, Dec 07 2003

Keywords

Comments

Conjecture: No term is zero.
The conjecture is true: If p is a prime factor of n, k = (n^n)/p gives an upper bound. - James Rayman, Mar 01 2023

Links

Crossrefs

Cf. A090526, A090527, A090528.

Programs

  • Maple
    f:= proc(n) local t,k;
  t:= n^n;
  for k from 2 do if isprime(floor(t/k)) then return k fi od
end proc:
map(f, [$2..100]); # Robert Israel, Mar 02 2023
  • Mathematica
    lnk[n_]:=Module[{k=1,nn=n^n},While[!PrimeQ[Floor[nn/k]],k++];k]; Array[lnk,70,2] (* Harvey P. Dale, Nov 07 2022 *)
  • PARI
    a(n)=for(i=1,1000,if(isprime(floor((n^n)/i)),print1(i,",");break()))

A090526 Primes arising in A090525, or 0 if A090525(n) = 0.

Original entry on oeis.org

2, 13, 23, 347, 4241, 41177, 1677721, 9224297, 769230769, 17831979413, 156422814881, 43267872370321, 317485909301657, 10680338789777057, 348051774975651917, 23635436053895336119, 230095953656704898101
Offset: 2

Views

Author

Amarnath Murthy, Dec 07 2003

Keywords

Comments

Conjecture: No term is zero.
Conjecture is true: see A090525. - Robert Israel, Mar 02 2023

Links

Crossrefs

Cf. A090525, A090527, A090528.

Programs

  • Maple
    f:= proc(n) local t,k,s;
  t:= n^n;
  for k from 2 do s:= floor(t/k); if isprime(s) then return s fi od
end proc:
map(f, [$2..100]); # Robert Israel, Mar 02 2023
  • Mathematica
    Do[p = n^n; i = 2; While[ !PrimeQ[Floor[p/i]], i++ ]; Print[Floor[p/i]], {n, 2, 30}] (* Ryan Propper, Aug 02 2005 *)

Formula

a(n) = floor(n^n/A090525(n)). - Robert Israel, Mar 02 2023

Extensions

More terms from Ryan Propper, Aug 02 2005
Offset corrected by Robert Israel, Mar 02 2023
Showing 1-3 of 3 results.

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

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