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.

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A085149 Numbers k such that k!!!!! - 1 is prime.

Original entry on oeis.org

3, 4, 6, 7, 8, 12, 13, 14, 27, 28, 33, 35, 44, 50, 62, 64, 74, 88, 114, 140, 142, 242, 248, 262, 270, 284, 395, 473, 582, 600, 634, 707, 805, 882, 907, 1008, 1152, 1243, 1853, 2340, 2410, 2703, 2793, 3033, 3600, 3925, 4124, 4154, 6185, 6367, 7130, 9104, 9992
Offset: 1

Views

Author

Hugo Pfoertner, Jun 23 2003

Keywords

Comments

The search for multifactorial primes started by Ray Ballinger is now continued by a team of volunteers on the website of Ken Davis (see link).

Links

Crossrefs

Cf. A085157 (quintuple factorials), A085148.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 5] - 1] & ] (* Robert Price, Apr 19 2019 *)

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
a(54)-a(63) from Ken Davis link added to b-file by Robert Price, Sep 23 2012

A100013 Number of prime factors in n!+7 (counted with multiplicity).

Original entry on oeis.org

3, 3, 2, 1, 1, 1, 1, 3, 3, 3, 3, 2, 3, 3, 4, 2, 2, 3, 3, 5, 5, 5, 3, 4, 3, 2, 4, 5, 5, 4, 7, 6, 4, 4, 7, 2, 5, 4, 7, 4, 5, 3, 4, 6, 5, 4, 3, 3, 5, 6, 3, 5, 6, 3, 3, 7, 4, 5, 5, 2, 4, 4, 5, 4, 2, 4, 3, 5, 2, 5, 7, 4, 7, 5, 5, 3, 5, 4, 6, 6, 8, 5
Offset: 0

Views

Author

Jonathan Vos Post, Nov 18 2004

Keywords

Examples

			Example 1!+7 = 2^3 so a(1) = 3.
a(3) = a(4) = a(5) = a(6) = 1 because 3!+1 = 13, 4!+7 = 31, 5!+1 = 127, 6!+7 = 727 and these are all primes. a(11) = a(15) = a(16) = a(25) = a(35) = a(59) = 2 because 11!+7 = 39916807 = 7 * 5702401, 15!+7 = 1307674368007 = 7 * 186810624001, 16!+7 = 20922789888007 = 7 * 2988969984001, 25!+7 = 15511210043330985984000007 = 7 * 2215887149047283712000001, 35!+7 = 10333147966386144929666651337523200000007 = 7 *
1476163995198020704238093048217600000001 and 59!+7 = 138683118545689835737939019720389406345902876772687432540821294940160000000000007 = 7 * 19811874077955690819705574245769915192271839538955347505831613562880000000000001 are all semiprimes.

References

  • C. Caldwell and H. Dubner, "Primorial, factorial and multifactorial primes," Math. Spectrum, 26:1 (1993/4) 1-7.

Links

Crossrefs

Cf. A002981, A037083, A037083, A085150, A085148, A085146, A062701, A055487, A062702.

Extensions

More terms from Sean A. Irvine, Sep 20 2012

A288718 Primes of the form k!5+1, where k!5 is the quintuple factorial number (A085157).

Original entry on oeis.org

2, 3, 5, 7, 37, 67, 313, 751, 2857, 129169, 576577, 17873857, 54286849, 393750001, 643458817, 19053977918977, 206180145819649, 11716249122484566383298871297, 177636555893291390456871518209, 49055724379818682505120501943238657
Offset: 1

Views

Author

Robert Price, Jun 13 2017

Keywords

Links

Crossrefs

Cf. A085148.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 5] + 1, {i, 0, 100}], PrimeQ[#]&]
Previous Showing 11-13 of 13 results.

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

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