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 1-5 of 5 results.

A231119 Least positive k such that n * k^k + 1 is a prime, or 0 if no such k exists.

Original entry on oeis.org

1, 1, 2, 1, 102414, 1, 2, 17, 2, 1, 36, 1, 2, 3, 2, 1, 210, 1, 20, 3, 990, 1, 6, 2, 2, 6, 2, 1
Offset: 1

Views

Author

Alex Ratushnyak, Nov 04 2013

Keywords

Comments

The number a(5) is conjectured to be zero. Four days of computation have shown that all numbers 5*k^k+1 are composite for k = 1..22733. - T. D. Noe, Nov 11 2013
The sum of 1/log(n*k^k) diverges slowly for every n so normal heuristics predict infinitely many primes in each case, including n=5. - Jens Kruse Andersen, Jun 16 2014
a(5) > 100000 or a(5) = 0. a(29) > 100000 or a(29) = 0. - Jason Yuen, Jan 06 2025
a(5) = 102414 . - Phillip Poplin, May 27 2025
a(29) > 150000 or a(29) = 0. - Phillip Poplin, May 27 2025

Crossrefs

Cf. A035093, A057217, A175763, A228175.

Programs

  • Java
    import java.math.BigInteger; public class A231119 { public static void main (String[] args) { for (int n = 1; n < 3333; n++) { BigInteger nn = BigInteger.valueOf(n); for (int k=1; k<10000; k++) { BigInteger p = nn.multiply(BigInteger.valueOf(k).pow(k)).add(BigInteger.ONE); if (p.isProbablePrime(80)) { System.out.printf("%d, ", k); break; } else System.out.printf("."); } } } }

Extensions

a(5) from Phillip Poplin, May 27 2025

A231819 Least positive k such that k*n^2 - 1 is a prime, or 0 if no such k exists.

Original entry on oeis.org

3, 1, 2, 2, 6, 2, 2, 2, 8, 2, 2, 3, 2, 3, 2, 5, 2, 2, 8, 5, 2, 2, 8, 2, 2, 3, 6, 2, 12, 3, 8, 5, 10, 2, 6, 2, 12, 2, 2, 3, 2, 2, 2, 3, 2, 2, 18, 3, 2, 2, 8, 2, 20, 3, 6, 2, 18, 3, 2, 3, 12, 2, 2, 2, 6, 7, 8, 6, 2, 3, 14, 3, 2, 3, 6, 2, 6, 3, 8, 2, 2, 5, 6, 5, 2
Offset: 1

Views

Author

Alex Ratushnyak, Nov 13 2013

Keywords

Crossrefs

Cf. A035092 (least k such that k*(n^2)+1 is a prime).
Cf. A175763 (least k such that k*(n^n)+1 is a prime).
Cf. A035093 (least k such that k*n!+1 is a prime).
Cf. A193807 (least k such that n*(k^2)+1 is a prime).
Cf. A231119 (least k such that n*(k^k)+1 is a prime).
Cf. A057217 (least k such that n*k!+1 is a prime).
Cf. A034693 (least k such that n*k +1 is a prime).
Cf. A231818 (least k such that k*(n^n)-1 is a prime).
Cf. A083663 (least k such that k*n!-1 is a prime).
Cf. A231734 (least k such that n*(k^2)-1 is a prime).
Cf. A231735 (least k such that n*(k^k)-1 is a prime).
Cf. A231820 (least k such that n*k!-1 is a prime).
Cf. A053989 (least k such that n*k -1 is a prime).

Programs

  • Mathematica
    Table[k = 1; While[! PrimeQ[k*n^2 - 1], k++]; k, {n, 100}] (* T. D. Noe, Nov 18 2013 *)

A070855 Smallest prime of the form k*n^n + 1.

Original entry on oeis.org

2, 5, 109, 257, 37501, 139969, 3294173, 167772161, 3874204891, 30000000001, 24536803672547, 17832200896513, 12115004263690121, 344472211592298497, 12261028930664062501, 221360928884514619393, 6617922095090694113417
Offset: 1

Views

Author

Amarnath Murthy, May 15 2002

Keywords

Comments

By Linnik's theorem, a(n) = O(n^(Ln)) for some effectively computable L.
For more terms, see A175763.

Links

Crossrefs

Cf. A121270, A110932, A175763.

Programs

  • Mathematica
    sp[n_]:=Module[{n2=n^n,k=1},While[!PrimeQ[k*n2+1],k++];k*n2+1]; Array[ sp,20] (* Harvey P. Dale, Jul 06 2014 *)

Extensions

More terms from Don Reble, May 16 2002
Comments and b-file from Charles R Greathouse IV, Aug 30 2010

A231820 Least positive k such that n*k! - 1 is a prime, or 0 if no such k exists.

Original entry on oeis.org

3, 2, 1, 1, 3, 1, 2, 1, 2, 2, 4, 1, 4, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 1, 3, 5, 2, 3, 3, 1, 2, 1, 3, 2, 4, 2, 2, 1, 3, 2, 4, 1, 3, 1, 2, 4, 3, 1, 2, 6, 2, 2, 3, 1, 2, 5, 2, 3, 3, 1, 10, 1, 4, 2, 3, 2, 3, 1, 2, 2, 7, 1, 8, 1, 2, 2, 3, 3, 2, 1, 5, 2, 8, 1, 3, 4, 2, 4, 15, 1
Offset: 1

Views

Author

Alex Ratushnyak, Nov 13 2013

Keywords

Links

Crossrefs

Cf. A035092 (least k such that k*(n^2)+1 is a prime).
Cf. A175763 (least k such that k*(n^n)+1 is a prime).
Cf. A035093 (least k such that k*n!+1 is a prime).
Cf. A193807 (least k such that n*(k^2)+1 is a prime).
Cf. A231119 (least k such that n*(k^k)+1 is a prime).
Cf. A057217 (least k such that n*k!+1 is a prime).
Cf. A034693 (least k such that n*k +1 is a prime).
Cf. A231819 (least k such that k*(n^2)-1 is a prime).
Cf. A231818 (least k such that k*(n^n)-1 is a prime).
Cf. A083663 (least k such that k*n!-1 is a prime).
Cf. A231734 (least k such that n*(k^2)-1 is a prime).
Cf. A231735 (least k such that n*(k^k)-1 is a prime).
Cf. A053989 (least k such that n*k -1 is a prime).

Programs

  • Maple
    f:= proc(n) local k;
for k from 1 do if isprime(n*k!-1) then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Oct 29 2019
  • Mathematica
    Table[k = 1; While[! PrimeQ[k!*n - 1], k++]; k, {n, 100}] (* T. D. Noe, Nov 18 2013 *)
  • PARI
    a(n) = my(k=1); while (!isprime(n*k! - 1), k++); k; \\ Michel Marcus, Oct 29 2019

A231818 Least positive k such that k*n^n - 1 is a prime, or 0 if no such k exists.

Original entry on oeis.org

3, 1, 2, 5, 6, 3, 6, 39, 18, 6, 12, 19, 8, 23, 10, 3, 76, 13, 90, 26, 52, 45, 124, 12, 60, 27, 10, 99, 126, 11, 50, 27, 28, 59, 6, 80, 122, 71, 110, 21, 72, 111, 590, 147, 178, 84, 238, 12, 138, 236, 10, 53, 6, 60, 98, 72, 620, 30, 166, 5, 98, 18, 22, 384, 126
Offset: 1

Views

Author

Alex Ratushnyak, Nov 13 2013

Keywords

Crossrefs

Cf. A035092 (least k such that k*(n^2)+1 is a prime).
Cf. A175763 (least k such that k*(n^n)+1 is a prime).
Cf. A035093 (least k such that k*n!+1 is a prime).
Cf. A193807 (least k such that n*(k^2)+1 is a prime).
Cf. A231119 (least k such that n*(k^k)+1 is a prime).
Cf. A057217 (least k such that n*k!+1 is a prime).
Cf. A034693 (least k such that n*k +1 is a prime).
Cf. A231819 (least k such that k*(n^2)-1 is a prime).
Cf. A083663 (least k such that k*n!-1 is a prime).
Cf. A231734 (least k such that n*(k^2)-1 is a prime).
Cf. A231735 (least k such that n*(k^k)-1 is a prime).
Cf. A231820 (least k such that n*k!-1 is a prime).
Cf. A053989 (least k such that n*k -1 is a prime).

Programs

  • Mathematica
    Table[k = 1; While[! PrimeQ[k*n^n - 1], k++]; k, {n, 65}] (* T. D. Noe, Nov 15 2013 *)
Showing 1-5 of 5 results.

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