A115786 Smallest prime number p such that p + 2#, p + 3#, ..., p + prime(n)# are all prime, where x# = A034386(x) is the primorial.

3, 5, 11, 17, 41, 41, 41, 41, 86351, 86351, 235313357, 729457511, 99445156397, 818113387907, 7986903815771, 29065965967667

Offset: 1

Author

Rick L. Shepherd, Jan 31 2006

Keywords

• more
• nonn

Comments

Subset of A001359 (lesser of twin primes).

From a(2) = 5 on, also a subset of A022004: first element of prime triples (p, p+2, p+6).-- It could make sense to add a(0) = 2, the smallest prime (with empty further restriction "p + prime(n)# prime for 1 <= n <= 0"). - M. F. Hasler, Apr 29 2015

Examples

			a(11) = 235313357 because 235313357, 235313357 + 2, 235313357 + 2*3, 235313357 + 2*3*5, ... and 235313357 + 2*3*5*7*11*13*17*19*23*29*31 are all prime and there is no smaller prime with this property.
		

Links

• C. Rivera, Puzzle 782: Prime-Generating non-polynomials, primepuzzles.net, April 4, 2015
• C. Rivera, Puzzle 350. Primes & primorials, primepuzzles.net, 2006

Crossrefs

Cf. A001359, A002110, A115785 (for p - p(i)#).

Extensions

a(12) from Don Reble, Feb 15 2006

More terms from Jens Kruse Andersen, Feb 28 2006