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A284754 a(n) is the smallest number k such that prime(k) divides primorial(j) + 1 for exactly n integers j.

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%I A284754 #13 Apr 03 2017 17:11:18
%S A284754 1,59,436,995752,180707
%N A284754 a(n) is the smallest number k such that prime(k) divides primorial(j) + 1 for exactly n integers j.
%C A284754 As used here, "primorial(j)" refers to the product of the first j primes, i.e., A002110(j).
%C A284754 Primorial(j) + 1 is the j-th Euclid number, A006862(j).
%C A284754 a(n) > 10^7 for n > 5. - _Giovanni Resta_, Apr 03 2017
%e A284754 a(1) = 1 because the first prime, prime(1) = 2, divides primorial(j) + 1 for exactly one integer j, namely, j = 0 (since primorial(0) = 1).
%e A284754 a(2) = 59 because prime(59) = 277 divides primorial(j) + 1 for exactly two integers j (i.e., 7 and 17), and 59 is the smallest integer for which this is the case.
%e A284754 a(3) = 436 because prime(436) = 3041 divides primorial(j) + 1 for exactly three integers j (i.e., 206, 263, and 409), and 436 is the smallest integer for which this is the case.
%e A284754 a(5) = 180707 because prime(180707) = 2464853 divides primorial(j) + 1 for exactly five integers j (i.e., 75366, 79914, 139731, 139990, and 175013), and 180707 is the smallest integer for which this is the case.
%Y A284754 Cf. A000040, A002110, A006862, A113165, A279097, A279098, A279099, A283928.
%K A284754 nonn,more
%O A284754 1,2
%A A284754 _Jon E. Schoenfield_, Apr 01 2017
%E A284754 a(4) from _Giovanni Resta_, Apr 02 2017