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

1,1

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

Links

Table of n, a(n) for n=1..16.

C. Rivera, Puzzle 782: Prime-Generating non-polynomials, primepuzzles.net, April 4, 2015

C. Rivera, Puzzle 350. Primes & primorials, primepuzzles.net, 2006

Example

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.

Crossrefs

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

Sequence in context: A125557 A007455 A034729 * A252089 A128550 A096479

Adjacent sequences: A115783 A115784 A115785 * A115787 A115788 A115789

Keyword

more,nonn

Author

Rick L. Shepherd, Jan 31 2006

Extensions

a(12) from Don Reble, Feb 15 2006

More terms from Jens Kruse Andersen, Feb 28 2006

Status

approved