

A084438


Positive integers n such that n!!!  1 = A007661(n)  1 is prime.


59



3, 4, 6, 8, 20, 26, 36, 50, 60, 114, 135, 138, 248, 315, 351, 429, 642, 5505, 8793, 12086, 13580, 23109, 34626, 34706, 56282, 57675, 58298
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OFFSET

1,1


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

Table of n, a(n) for n=1..27.
Ken Davis, Status of Search for Multifactorial Primes.
Ken Davis, Results for n!31.
ProthSearch.net (on web.archive.org), n3minus.txt


EXAMPLE

a(4)=8 since 8!!!1 = 8*5*21 = 79 is the 4th prime of that form.
26!!!1 = 2504902399 is prime.


MATHEMATICA

multiFactorial[n_, k_] := If[n < 1, 1, n * multiFactorial[n  k, k]];
Select[Range[0, 1000], PrimeQ[multiFactorial[#, 3]  1] & ] (* Robert Price, Apr 19 2019 *)
Select[Range[650], PrimeQ[Times @@ Range[#, 1, 3]  1] &] (* The program generates the first 17 terms of the sequence. To generate more, change the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, May 22 2021 *)


PROG

(PARI) A007661(n) = prod(i=1, (n1)\3, n=3, n+!n) /* newline */ for(n=1, 999, if(isprime(A007661(n)1), print1(n", ")))  M. F. Hasler, Nov 26 2007


CROSSREFS

Cf. A007661, A135726, A037082, A037083.
Sequence in context: A134580 A007749 A063506 * A186700 A028987 A284615
Adjacent sequences: A084435 A084436 A084437 * A084439 A084440 A084441


KEYWORD

hard,nonn


AUTHOR

Hugo Pfoertner, Jun 25 2003


EXTENSIONS

Missing 26 inserted by M. F. Hasler, Nov 26 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Edited by N. J. A. Sloane, Feb 11 2009 at the suggestion of M. F. Hasler


STATUS

approved



