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Numbers k such that k![6]-2 is prime, where k![6] = A085158 (k) = sextuple factorial.
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%I #16 Apr 03 2023 10:36:13

%S 4,5,7,11,13,23,25,31,33,37,59,63,91,157,265,267,327,539,555,621,715,

%T 921,979,1633,1821,2259,2697,2809,2863,2935,4213,4351,5937,6885,8743,

%U 10761,15159,17685,52075,55147,68677,99655

%N Numbers k such that k![6]-2 is prime, where k![6] = A085158 (k) = sextuple factorial.

%C a(43) > 10^5.

%C The first 10 primes associated with this sequence: 2, 3, 5, 53, 89, 21503, 43223, 1339973, 7577953, 49579073.

%H C. Caldwell and H. Dubner (Eds): <a href="https://t5k.org/lists/top_ten/">The top ten prime numbers: from the unpublished collections of R. Ondrejka</a> (May 2001), Table 21 F, p. 75

%H Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.

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

%t Select[Range[2, 50000], PrimeQ[MultiFactorial[#, 6] - 2] &]

%t Select[Range[100000],PrimeQ[Times@@Range[#,1,-6]-2]&] (* _Harvey P. Dale_, Feb 23 2023 *)

%Y Cf. A076185, A085158, A094144, A204657.

%K nonn

%O 1,1

%A _Robert Price_, Mar 08 2017

%E a(39)-a(42) from _Robert Price_, Jul 09 2017