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A204657 Numbers n such that n!10 + 2 is prime.

%I A204657 #30 Apr 03 2023 10:36:12
%S A204657 0,1,3,5,9,11,13,19,21,25,41,57,79,127,135,149,165,177,193,209,223,
%T A204657 255,273,287,297,375,433,459,481,565,1079,1435,1543,1771,1913,1983,
%U A204657 2063,2305,2653,6789,8757,11149,13671,15433,16369,17261,18129,22129,22785,22875,25235,25247,26329,27675,33391,39075,41195,47435,47621,48409,59235,59715,61571,65433,78761,83033
%N A204657 Numbers n such that n!10 + 2 is prime.
%C A204657 n!10 = Product_{k=0..floor((n-1)/10)}(n - 10k).
%C A204657 a(61) > 50000. - _Robert Price_, Jun 10 2012
%C A204657 The first 11 primes associated with this sequence: 3, 3, 5, 7, 11, 13, 41, 173, 233, 1877, 293603. - _Robert Price_, Mar 10 2017
%C A204657 a(67) > 10^5. - _Robert Price_, Mar 31 2017
%H A204657 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The top ten prime numbers: from the unpublished collections of R. Ondrejka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 A204657 Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.
%H A204657 Nathan Russell, <a href="http://groups.yahoo.com/group/primenumbers/message/23995">n!10+2 results</a>, primenumbers group, Jan 2012.
%H A204657 Nathan Russell, <a href="/A204656/a204656.txt">n!10+2 results</a>, message 23995 in primenumbers Yahoo group, Jan 17, 2012.
%t A204657 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A204657 Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 10] + 2] &]
%o A204657 (PARI) for(n=0,9999,isprime(prod(i=0,(n-2)\10,n-10*i)+2)& print1(n","))
%Y A204657 Cf. A204658, A204659, A204660, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.
%K A204657 nonn,hard
%O A204657 1,3
%A A204657 _M. F. Hasler_, Jan 17 2012
%E A204657 a(40)-a(59) from _Robert Price_, Jun 10 2012
%E A204657 Inserted missing term of 6789 by _Robert Price_, Mar 10 2017
%E A204657 a(61)-a(66) from _Robert Price_, Mar 31 2017