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.

A208276 Number of Poulet numbers (or pseudoprimes to base 2, A001567) less than 2^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 8, 13, 19, 32, 45, 64, 89, 124, 175, 251, 361, 502, 693, 944, 1264, 1713, 2361, 3169, 4232, 5749, 7750, 10403, 14011, 18667, 24958, 33389, 44540, 59565, 79343, 105659, 141147, 188231, 250568, 333737, 445316, 593366, 792172, 1059097, 1416055, 1893726, 2532703, 3390284, 4540673, 6086093, 8167163, 10964612, 14731767, 19806649, 26651383, 35893886, 48374139, 65247459, 88069251, 118968378
Offset: 1

Views

Author

Washington Bomfim, Feb 25 2012

Keywords

Links

Crossrefs

Cf. A001567, A055550, A108797, A225005

Programs

  • PARI
    count=0;for(e=1,32,forcomposite(n=2^(e-1),2^e-1,if(n%2 && Mod(2,n)^(n-1)==1,count++)); print1(count", ")); \\ Hans Loeblich, May 15 2019

Extensions

a(50)-a(64) from Feitsma's website, added by Max Alekseyev, Apr 23 2013

A114249 Number of Fermat pseudoprimes to base 7 less than 10^n.

Original entry on oeis.org

1, 2, 6, 16, 73, 234, 659, 1797, 4950, 13070, 33989, 87448
Offset: 1

Views

Author

Eric W. Weisstein, Nov 18 2005

Keywords

Links

Crossrefs

Cf. A005938, A055550, A114245, A114247.

Programs

  • Mathematica
    Table[Count[Select[Range[2, 10^6], ! PrimeQ[#] && PowerMod[7, # - 1, #] == 1 &], x_ /; x < 10^n], {n, 6}]  (* Robert Price, Jun 09 2019 *)

Extensions

a(9)-a(12) from Hiroaki Yamanouchi, Sep 25 2015

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)

A300418 Number of semiprime Fermat pseudoprimes to base 2 (A214305) less than 10^n.

Original entry on oeis.org

0, 0, 1, 11, 34, 107, 312, 882, 2457, 6504, 17206, 46073, 123868, 334567, 915443, 2520503, 7002043, 19604493, 55264235
Offset: 1

Views

Author

Amiram Eldar, Mar 05 2018

Keywords

Links

Crossrefs

Cf. A055550, A214305.

Extensions

Corrected and extended by Daniel Suteu, Dec 10 2019
Showing 1-4 of 4 results.

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

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