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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A051592 Numbers k such that k!!!!!! - 1 is prime.

Original entry on oeis.org

3, 4, 6, 12, 14, 54, 74, 102, 114, 302, 318, 366, 614, 1178, 1188, 3110, 7284, 21432, 21906, 25848, 29882, 38618, 41990, 84510, 86022
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

k!!!!!! = k*(k-6)*(k-12)*(k-18)*...
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. A085158 (sextuple factorials), A085150.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 6] - 1] & ] (* Robert Price, Apr 19 2019 *)

Extensions

Edited and extended by Hugo Pfoertner, Jun 23 2003
Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

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

A114796 Cumulative product of sextuple factorial A085158.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 5040, 80640, 2177280, 87091200, 4790016000, 344881152000, 31384184832000, 7030057402368000, 2847173247959040000, 1822190878693785600000, 1703748471578689536000000
Offset: 0

Views

Author

Jonathan Vos Post, Feb 18 2006

Keywords

Examples

			a(10) = 1!6 * 2!6 * 3!6 * 4!6 * 5!6 * 6!6 * 7!6 * 8!6 * 9!6 * 10!6
= 1 * 2 * 3 * 4 * 5 * 6 * 7 * 16 * 27 * 40 = 87091200 = 2^11 * 3^5 * 5^2 * 7.
Note that a(10) + 1 = 87091201 is prime, as is a(9) + 1 = 2177281.

Links

Crossrefs

Cf. A000178, A006882, A007662, A085150, A085157, A085158, A114347.

Programs

  • GAP
    b:= function(n)
    if n<1 then return 1;
    else return n*b(n-6);
    fi;
  end;
List([0..20], n-> Product([0..n], j-> b(j)) ); # G. C. Greubel, Aug 22 2019
  • Magma
    b:=func< n | n le 6 select n else n*Self(n-6) >;
[1] cat [(&*[b(j): j in [1..n]]): n in [1..20]]; // G. C. Greubel, Aug 22 2019
  • Maple
    b:= n-> `if`(n<1, 1, n*b(n-5)); a:= n-> product(b(j), j = 0..n); seq(a(n), n = 0..20); # G. C. Greubel, Aug 22 2019
  • Mathematica
    b[n_]:= b[n]= If[n<1, 1, n*b[n-6]]; a[n_]:= Product[b[j], {j,0,n}];
Table[a[n], {n, 0, 20}] (* G. C. Greubel, Aug 22 2019 *)
  • PARI
    b(n)=if(n<1, 1, n*b(n-6));
vector(20, n, n--; prod(j=0,n, b(j)) ) \\ G. C. Greubel, Aug 22 2019
  • Sage
    def b(n):
    if (n<1): return 1
    else: return n*b(n-6)
[product(b(j) for j in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 22 2019

Formula

a(n) = Product_{j=0..n} j!!!!!!.
a(n) = Product_{j=0..n} j!6.
a(n) = Product_{j=0..n} A085158(j).
a(n) = n!!!!!! * a(n-1) where a(0) = 1, a(1) = 1 and n >= 2.
a(n) = n*(n-6)!!!!!! * a(n-1) where a(0) = 1, a(1) = 1, a(2) = 2.
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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