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.

A055550 Number of Poulet numbers (or pseudoprimes to base 2, A001567) less than 10^n.

Original entry on oeis.org

0, 0, 3, 22, 78, 245, 750, 2057, 5597, 14884, 38975, 101629, 264239, 687007, 1801533, 4744920, 12604009, 33763684, 91210364
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

References

  • J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 245, pp 68, Ellipses, Paris 2008. - Lekraj Beedassy, Jul 20 2008
  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 219.

Links

Crossrefs

Cf. A001567, A055552.

Programs

  • Mathematica
    Table[Count[Select[Range[2, 10^6], ! PrimeQ[#] && PowerMod[2, # - 1, #] == 1 &], x_ /; x < 10^n], {n, 6}]  (* Robert Price, Jun 09 2019 *)

Extensions

a(14) and a(15) computed by William F. Galway and communicated by Arthur Livingstone (arthur.livingstone(AT)gmail.com), Apr 10 2007
Edited by N. J. A. Sloane, Feb 01 2009 at the suggestion of Charles R Greathouse IV
a(14)-a(15) recomputed (were missing) and a(16)-a(19) added by Charles R Greathouse IV, Jan 28 2011, based on the calculations of Jan Feitsma

A108797 Number of base-2 strong pseudoprimes (A001262) less than 2^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 4, 6, 7, 11, 18, 24, 34, 49, 75, 104, 147, 210, 296, 409, 552, 734, 981, 1311, 1736, 2314, 3093, 4139, 5511, 7396, 9835, 13106, 17493, 23270, 31115, 41664, 55763, 74739, 100342, 134559, 180725, 243566, 327731, 441270, 594585, 803252, 1085426, 1468777, 1988905, 2697846, 3662239, 4976375, 6767707, 9212942, 12552513, 17114780, 23355139, 31894014
Offset: 1

Views

Author

Charles R Greathouse IV, Dec 03 2005

Keywords

Examples

			a(12)=3 since 2047, 3277 and 4033 are the 2-SPSPs less than 4096.

Links

Crossrefs

Cf. A001262, A055552, A208276

Extensions

a(24)-a(64) from Charles R Greathouse IV, Jan 28 2011, based on the calculations of Jan Feitsma.
a(1)=...=a(10)=0 prepended by Max Alekseyev, Apr 23 2013

A055551 Number of base-2 Euler-Jacobi pseudoprimes (A047713) less than 10^n.

Original entry on oeis.org

0, 0, 1, 12, 36, 114, 375, 1071, 2939, 7706, 20417, 53332, 139597, 364217, 957111, 2526795, 6725234, 18069359, 48961462
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

Pomerance et al. gave the terms a(3)-a(10). Pinch gave the terms a(4)-a(13), but a(13)=124882 was wrong. He later calculated the correct value, which appears in Guy's book. - Amiram Eldar, Nov 08 2019

Examples

			Below 10^3 there is only one Euler-Jacobi pseudoprime, 561. Therefore a(3) = 1.

References

  • Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, section A12, p. 44.
  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 219.

Links

Crossrefs

Cf. A047713, A055550, A055552.

Programs

  • Mathematica
    ejpspQ[n_] := CompositeQ[n] && PowerMod[2, (n - 1)/2, n] == Mod[JacobiSymbol[2, n], n]; s = {}; c = 0; p = 10; n = 1; Do[If[ejpspQ[n], c++]; If[n > p, AppendTo[s, c]; p *= 10], {n, 1, 1000001, 2}]; s (* Amiram Eldar, Nov 08 2019 *)

Extensions

a(13) corrected and a(14)-a(19) added by Amiram Eldar, Nov 08 2019 (calculated from Feitsma & Galway's tables)
Showing 1-3 of 3 results.

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

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