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

1, 59, 436, 995752, 180707

Offset: 1

Author

Jon E. Schoenfield, Apr 01 2017

Keywords

• nonn
• more

Comments

As used here, "primorial(j)" refers to the product of the first j primes, i.e., A002110(j).

Primorial(j) + 1 is the j-th Euclid number, A006862(j).

a(n) > 10^7 for n > 5. - Giovanni Resta, Apr 03 2017

Examples

			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).
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.
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.
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.
		

Crossrefs

Cf. A000040, A002110, A006862, A113165, A279097, A279098, A279099, A283928.

Extensions

a(4) from Giovanni Resta, Apr 02 2017