The On-Line Encyclopedia of Integer Sequences (OEIS)

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Numbers n such that n!!! - 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661)..
(history; published version)

#6 by N. J. A. Sloane at Sat Dec 05 00:09:51 EST 2015

STATUS

proposed

approved

#5 by Altug Alkan at Fri Dec 04 12:09:29 EST 2015

STATUS

editing

proposed

#4 by Altug Alkan at Fri Dec 04 12:08:50 EST 2015

PROG

(PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);

for(n=1, 1e4, if(ispseudoprime(tf(n) - 3^10), print1(n , ", "))) \\ Altug Alkan, Dec 04 2015

STATUS

proposed

editing

#3 by Robert Price at Fri Dec 04 11:59:33 EST 2015

STATUS

editing

proposed

#2 by Robert Price at Fri Dec 04 11:58:42 EST 2015

NAME

allocated for Robert PriceNumbers n such that n!!! - 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661)..

DATA

19, 20, 22, 26, 41, 55, 56, 152, 155, 316, 347, 383, 500, 556, 646, 656, 748, 976, 1433, 2213, 2680, 2911, 3373, 4799, 4964, 7189, 8798, 9871, 14069, 14627, 16657, 20230, 24137, 24430, 28331, 36313, 41522, 43031, 46072, 47719

OFFSET

1,1

COMMENTS

Corresponding primes are 1047511, 4129751, 24285271, 2504843351, 126757680265156951, ... .

a(41) > 50000.

LINKS

Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-59049&action=Search">PRP Records. Search for n!3-59049.</a>

Joe McLean, <a href="http://web.archive.org/web/20091027034731/http://uk.geocities.com/nassarawa%40btinternet.com/probprim2.htm">Interesting Sources of Probable Primes</a>

EXAMPLE

19!3 - 3^10 = 19*16*13*10*7*4*1 - 59049 = 1047511 is prime, so 19 is in the sequence.

MATHEMATICA

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];

Select[Range[17, 50000], PrimeQ[MultiFactorial[#, 3] - 3^10] &]

CROSSREFS

Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772, A261145.

KEYWORD

allocated

hard,more,nonn

AUTHOR

Robert Price, Dec 04 2015

STATUS

approved

editing

#1 by Robert Price at Fri Dec 04 11:58:42 EST 2015

NAME

allocated for Robert Price

KEYWORD

allocated

STATUS

approved