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 1-4 of 4 results.

A187605 Primes of the form k^k + k - 1.

Original entry on oeis.org

5, 29, 1978419655660313589123997, 205891132094649000000000000000000000000000029
Offset: 1

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Author

Marco Ripà, Mar 11 2011

Keywords

Comments

See A058912 for numbers k such that k^k + k - 1 is prime. Subsequence of A231712 (numbers n^n + n - 1). - Jaroslav Krizek, Nov 13 2013
The next prime has 1460 digits. - Jinyuan Wang, Mar 01 2020

Crossrefs

Programs

  • Mathematica
    Do[p=n^n+n-1; If[PrimeQ[p], Print[p]], {n, 100}]
  • PARI
    lista(nn) = for(k=1, nn, if(ispseudoprime(q=k^k+k-1), print1(q, ", "))); \\ Jinyuan Wang, Mar 01 2020

A342449 a(n) = Sum_{k=1..n} gcd(k,n)^k.

Original entry on oeis.org

1, 5, 29, 262, 3129, 46705, 823549, 16777544, 387421251, 10000003469, 285311670621, 8916100581446, 302875106592265, 11112006826387025, 437893890391180013, 18446744073743123788, 827240261886336764193, 39346408075299116257065
Offset: 1

Views

Author

Seiichi Manyama, Mar 13 2021

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := Sum[GCD[k, n]^k, {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)
  • PARI
    a(n) = sum(k=1, n, gcd(k, n)^k);

Formula

If p is prime, a(p) = p-1 + p^p = A231712(p).

A357055 Integers k such that k^k + k^2 + 3*k + 2 is prime.

Original entry on oeis.org

0, 1, 3, 5, 11, 209, 1281
Offset: 1

Views

Author

Marco Ripà, Sep 10 2022

Keywords

Comments

a(8) > 20000, if it exists. - Michael S. Branicky, Sep 17 2024

Examples

			For k = 3, k^k + k^2 + 3*k + 2 = 47 and 47 is prime.
		

Crossrefs

Programs

  • PARI
    isok(k) = ispseudoprime(k^k + k^2 + 3*k + 2); \\ Michel Marcus, Sep 10 2022

A357056 Integers k such that k^k + k^2 + 2*k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 9, 10, 13, 15, 24
Offset: 1

Views

Author

Marco Ripà, Sep 10 2022

Keywords

Comments

The next prime (if any) is unknown, but it must exceed 2000^2000 + 2000^2 + 2*2000 + 1 (a 6603-digit number).
a(11) > 15000, if it exists. - Michael S. Branicky, Sep 17 2024

Examples

			If k = 2, then k^k + k^2 + k*2 + 1 = 2^2 + 2^2 + 2*2 + 1 = 13, which is prime.
		

Crossrefs

Showing 1-4 of 4 results.