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.

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 *)

A231734 Least k such that n*k^2 - 1 is a prime, or 0 if no such k exists.

Original entry on oeis.org

2, 2, 1, 1, 2, 1, 6, 1, 0, 3, 2, 1, 6, 1, 2, 0, 2, 1, 6, 1, 2, 3, 4, 1, 0, 2, 2, 3, 4, 1, 12, 1, 2, 6, 2, 0, 18, 1, 14, 3, 2, 1, 18, 1, 2, 27, 4, 1, 0, 2, 10, 3, 2, 1, 6, 2, 2, 3, 20, 1, 12, 1, 2, 0, 4, 2, 6, 1, 4, 9, 2, 1, 30, 1, 6, 3, 2, 2, 6, 1, 0, 12, 2, 1, 12, 3, 2
Offset: 1

Views

Author

Alex Ratushnyak, Nov 12 2013

Keywords

Examples

			a(9)=0 because 9*k^2-1 is never a prime: (3k-1)*(3k+1).

Links

Crossrefs

Cf. A000040, A193807.

Programs

  • PARI
    a(n) = if (issquare(n) && (n>=9), 0, my(k=1); while (!isprime(n*k^2 - 1), k++); k); \\ Michel Marcus, Aug 20 2019

A231735 Least positive k such that n*k^k - 1 is a prime, or 0 if no such k exists.

Original entry on oeis.org

2, 2, 1, 1, 2, 1, 1128, 1, 0, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 14, 1, 0, 2, 2, 6, 206, 1, 1590, 1, 2, 11, 2, 3
Offset: 1

Views

Author

Alex Ratushnyak, Nov 12 2013

Keywords

Comments

From Gordon Atkinson, Aug 20 2019: (Start)
For all odd numbers n > 3, a(n) is even.
For all odd numbers n > 1, a(n^2) = 0. (End)
a(37) > 10^4. - Jinyuan Wang, Mar 05 2020
From Kevin P. Thompson, Feb 12 2023: (Start)
Other known terms: a(38) = 1, a(39) = 6, a(40) = 6, a(41) = 2, a(42) = 1, a(44) = 8, a(45) = 22, a(47) = 48, a(48) = 7, a(49) = 0, a(50) = 14.
Other unknown terms: a(43) > 5000, a(46) > 1000, a(51) > 1000. (End)
a(37) > 10^5, a(43) > 10^5, a(46) = 5430, a(51) = 4010. - Jason Yuen, Jan 19 2025
a(37) > 150000, a(43) > 323000. - Phillip Poplin, May 28 2025

Examples

			The least k > 0 such that 5*k^k - 1 is a prime is k = 2, so a(5) = 2.

Crossrefs

Cf. A000040, A008864, A193807, A231734.

Programs

  • Mathematica
    Table[If[And[n > 1, OddQ@ Sqrt@ n], 0, If[And[n > 3, OddQ@ n], Block[{k = 2}, While[! PrimeQ[n*k^k - 1], k += 2]; k], Block[{k = 1}, While[! PrimeQ[n*k^k - 1], k++]; k]]], {n, 36}] (* Michael De Vlieger, Sep 29 2019 *)
  • PARI
    a(n) = if(sqrt(n)%2==1 && n>1, 0, for(k=1, oo, if(ispseudoprime(n*k^k-1), return(k)))); \\ Jinyuan Wang, Mar 05 2020

Formula

a(A008864(k)) = 1. - Gordon Atkinson, Sep 04 2019

Extensions

a(9) and a(25) from Gordon Atkinson, Aug 20 2019
a(26)-a(36) from Alois P. Heinz, Aug 20 2019

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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