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.

A377367 Rectangular array by antidiagonals: R(m,n) = least k such that 2n*prime(m)^k + 1 is prime.

Original entry on oeis.org

1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 6, 4, 1, 1, 1, 10, 1, 1, 3, 1, 3, 1, 1, 2, 1, 1, 14, 1, 1, 2, 2, 3, 8, 3, 2, 1, 1, 1, 2, 1, 3, 3, 1, 11, 1, 1, 1, 1, 4, 2, 1, 1, 1, 2, 2, 4, 6, 5, 4, 1, 1
Offset: 1

Views

Author

Clark Kimberling, Oct 31 2024

Keywords

Examples

			Corner:
   1     1    1     2     1     1    1     3    2     1     1    1    1     3     2
   1     2    1     1     2     1    1     2    3     1     4    2    1     2     1
   1     1    1     4     1     1    3     3    1     1     1    8    1     3    11
   1     1    1    10     2     8    1     2    3     2     1    1    1     1     8
   1     1    1     1     3    11    2     1    2     4     1    8    1     1     1
   6     1    1     2     1     4    1    13    2     1     1    2    3     3     1
   3    14    1     1     6     1    1     3    1     1     8    1    4     2     3
   1     1    1     5     4     7    1    14    2     1     2    1    2     1     6
   1     1    4     1     3     2    1     2    3     2     5    1    6     1     2
   4     1    1     2     2     1    3     5    1     5     1    1    1     1     4
   1     1    2     3     1     2    3     2    3     1     9    1    3     1     1
   1     3    2     2     4     1    1     7    1    11     4    1    1    10     3
   1     1    2     3     3     1    1     3    1     1     1    2    1     1     2
   2     1    2     3     1     8    1     1    1     2     3    1    1     2     1
   1    16    1     4    11     1    4     3    3     2    18    1    2     4     2

Crossrefs

Cf. A000040, A377366.

Programs

  • Mathematica
    f[m_, n_, k_] := 2 n*Prime[m]^k + 1;
s[m_, n_] := Select[Range[20], PrimeQ[f[m, n, #]] &, 1]
u[m_] := Flatten[Table[s[m, n], {n, 1, 60}]]
Column[Table[Take[u[m], 16], {m, 2, 16}]]
r[m_] := Take[u[m], 12];
w[m_, n_] := r[m][[n]];
Table[w[m, n], {m, 1, 16}, {n, 1, 12}] (* array *)
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* sequence *)

A377364 a(n) = least k such that 2n*3^k-2 is prime, or 0 if no prime is reached.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 4, 5, 1, 2, 1, 2, 1, 1, 1, 9, 2, 1, 4, 1, 1, 2, 1, 5, 1, 1, 11, 1, 2, 2, 4, 3, 1, 1, 1, 3, 2, 4, 1, 1, 5, 3, 1, 1, 3, 1, 2, 4, 1, 1, 1, 2, 2, 1, 5, 1, 3, 1, 2, 1, 1, 8, 3, 1, 1, 4, 2, 80, 1, 6, 1, 8, 2, 2
Offset: 1

Views

Author

Clark Kimberling, Oct 31 2024

Keywords

Examples

			a(20) = 5 because 40*3^5 + 1 is prime and 40*3^k + 1 is not prime for k=1..4.

Crossrefs

Cf. A000040, A050412, A354747, A377365, A377366, A377367.

Programs

  • Mathematica
    {b, h} = {3, 2}; f[n_, k_] := n*b^k - h
s[n_] := Select[Range[20], PrimeQ[f[n, #]] &, 1]
Flatten[Table[s[n], {n, 1, 200}]]

A377365 a(n) = least k such that 2n*5^k+1 is prime, or 0 if no prime is reached.

Original entry on oeis.org

1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 4, 2, 1, 2, 1, 3, 8, 1, 1, 1036, 1, 3, 2, 1, 1, 2, 1, 1, 2, 4, 1, 2, 1, 3, 6, 2, 257, 2, 2, 1, 40, 1, 1, 4, 2, 1, 2, 10, 1, 4, 2, 1, 6, 1, 3, 2, 1, 15, 4, 1, 79, 48, 1, 1, 2, 1, 5, 6, 1, 1, 6, 4, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 6
Offset: 1

Views

Author

Clark Kimberling, Oct 31 2024

Keywords

Examples

			a(20) = 1036 because 40*5^k+1 is prime for k=1036 and not prime for k=1..1035.

Crossrefs

Cf. A000040, A050412, A354747, A377364, A377366, A377367.

Programs

  • Mathematica
    f[n_, k_] := 2 n*5^k + 1;
s[n_] := Select[Range[5000], PrimeQ[f[n, #]] &, 1];
Flatten[Table[s[n], {n, 1, 500}]]
Showing 1-3 of 3 results.

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

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