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.

A030660 Erroneous version of A046068.

Original entry on oeis.org

2, 5, 3, 4, 2, 3, 8, 2, 15, 10, 4, 9, 4, 4, 3, 60, 6, 3, 4, 2, 11, 6, 9, 1483, 6, 3, 5, 8, 3
Offset: 1

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Author

Keywords

A046067 Smallest m such that (2n-1)2^m+1 is prime, or -1 if no such value exists.

Original entry on oeis.org

0, 1, 1, 2, 1, 1, 2, 1, 3, 6, 1, 1, 2, 2, 1, 8, 1, 1, 2, 1, 1, 2, 2, 583, 2, 1, 1, 4, 2, 5, 4, 1, 1, 2, 1, 3, 2, 1, 3, 2, 1, 1, 4, 2, 1, 8, 2, 1, 2, 1, 3, 16, 1, 3, 6, 1, 1, 2, 3, 1, 8, 6, 1, 2, 3, 1, 4, 1, 3, 2, 1, 53, 6, 8, 3, 4, 1, 1, 8, 6, 3, 2, 1, 7, 2, 8, 1, 2, 2, 1, 4, 1, 3, 6, 1, 1, 2, 4, 15, 2
Offset: 1

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Author

Eric W. Weisstein

Keywords

Comments

There exist odd integers 2k-1 such that (2k-1)2^n+1 is always composite.
The smallest known example is 78557. Therefore a(39279) = -1.
For the corresponding primes see A057025(n-1), n >= 1, where a 0 will show up if a(n) = -1. - Wolfdieter Lang, Feb 07 2013.
Jaeschke shows that every positive integer appears infinitely often. - Jeppe Stig Nielsen, Jul 06 2020

References

  • Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 357-359, 1996.

Links

Crossrefs

Cf. A046068.
Bisection of A040076. Cf. A033809.
Cf. A057192, A057025.

Programs

  • Mathematica
    max = 10000 (* this maximum value of m is sufficient up to n = 1000 *); a[n_] := For[m = 1, m <= max, m++, If[PrimeQ[(2n - 1)*2^m + 1], Return[m]]] /. Null -> -1; a[1] = 0; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 08 2012 *)

A033809 Smallest m>0 such that (2n-1)2^m+1 is prime, or -1 if no such value exists.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 3, 6, 1, 1, 2, 2, 1, 8, 1, 1, 2, 1, 1, 2, 2, 583, 2, 1, 1, 4, 2, 5, 4, 1, 1, 2, 1, 3, 2, 1, 3, 2, 1, 1, 4, 2, 1, 8, 2, 1, 2, 1, 3, 16, 1, 3, 6, 1, 1, 2, 3, 1, 8, 6, 1, 2, 3, 1, 4, 1, 3, 2, 1, 53, 6, 8, 3, 4, 1, 1, 8, 6, 3, 2, 1, 7, 2, 8, 1, 2, 2, 1, 4, 1, 3, 6, 1, 1, 2, 4, 15, 2
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

There exist odd integers 2k-1 such that (2k-1)2^n+1 is always composite.

References

  • Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 357-359, 1996.

Links

Crossrefs

Cf. A046067 (except for initial term a(1) identical to this sequence), A046068, A046069, A046070.
Cf. A040076

A046070 Second smallest m such that (2n-1)2^m-1 is prime, or -1 if no such value exists.

Original entry on oeis.org

3, 1, 4, 5, 3, 26, 7, 2, 4, 3, 2, 6, 9, 2, 16, 5, 3, 6, 2553, 24, 10, 31, 2, 14, 5, 9, 6, 3, 2, 16, 5, 3, 6, 9, 4, 14, 11, 3, 4, 3, 5, 4, 11, 2, 8, 3, 4, 6, 9, 4, 18, 7, 3, 12, 149, 3, 14, 3, 2, 16, 3, 3, 4, 113, 3, 14, 11, 9, 18, 5, 2, 4, 13, 2, 16, 221, 4, 8, 5, 4, 6, 31, 3, 6, 5, 3, 4, 3
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

There exist odd integers 2k-1 such that (2k-1)2^n-1 is always composite.

References

  • Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 357-359, 1996.

Links

Crossrefs

Cf. A046068, A046069.

Programs

  • Mathematica
    max = 10000 (* this maximum value of m is sufficient up to n=168 *); a[n_] := Reap[ For[m = 0; cnt = 0, m <= max && cnt < 2, m++, If[m == max, Sow[-1], If[PrimeQ[(2*n - 1)*2^m - 1], cnt++; Sow[m]]]]][[2, 1]]; Table[a[n][[2]], {n, 1, 88}] (* Jean-François Alcover, Feb 28 2013 *)
Showing 1-4 of 4 results.

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