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A115786 Smallest prime number p such that p + 2#, p + 3#, ..., p + prime(n)# are all prime, where x# = A034386(x) is the primorial. 2
3, 5, 11, 17, 41, 41, 41, 41, 86351, 86351, 235313357, 729457511, 99445156397, 818113387907, 7986903815771, 29065965967667 (list; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified February 26 11:46 EST 2024. Contains 370352 sequences. (Running on oeis4.)