A114339 Numbers n such that 1/5 of the cumulative sum of the first n factorials of nonprimes is prime.

2, 3, 5, 6, 11, 22, 49, 58, 115, 125, 133, 151, 394, 645, 680

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Formula

n iff (1/5)*SUM[i=1 to n]A000142(A018252(i)) is in A000040. n iff (1/5)*SUM[i=1 to n]nonprime(i)! is in A000040.

Example

a(1) = 2 because (nonprime(1)!+nonprime(2)!)/5 = (1! + 4!)/5 = 25/5 = 5 is prime.
a(2) = 3 because (nonprime(1)!+nonprime(2)!+nonprime(3)!)/5 = (1! + 4! + 6!)/5 = 745/5 = 43 is prime.
a(3) = 5 because (1! + 4! + 6! + 8! + 9!)/5 = 40395/5 = 80789 is prime.
a(4) = 6 because (1! + 4! + 6! + 8! + 9! + 10!)/5 = 4032745/5 = 806549 is prime.
a(5) = 11 because (1! + 4! + 6! + 8! + 9! + 10! + 12! + 14! + 15! + 16! + 18!)/5 = 128498366261909 is prime.
a(6) = 22 because (1! + 4! + 6! + 8! + 9! + 10! + 12! + 14! + 15! + 16! + 18! + 20! + 21! + 22! + 24! + 25! + 26! + 27! + 28! + 30! + 32! + 33!)/5 =
1789342804960406115195785578904885909 is prime.
a(7) = 49 because (1! + 4! + 6! + 8! + 9! + 10! + 12! + 14! + 15! + 16! + 18! + 20! + 21! + 22! + 24! + 25! + 26! + 27! + 28! + 30! + 32! + 33! + 34! + 35! + 36! + 38! + 39! + 40! + 42! + 44! + 45! + 46! + 48! + 49! + 50! + 51! + 52! + 54! + 55! + 56! + 57! + 58! + 60! + 62! + 63! + 64! + 65! + 66! + 68!)/5 =
496117652785503784612715578829982325957792421778841808879262147120349639368839627755489688885909 is prime.

Crossrefs

Cf. A000040, A000142, A018252.

Sequence in context: A078913 A174100 A359599 * A339308 A127525 A179333

Adjacent sequences: A114336 A114337 A114338 * A114340 A114341 A114342

Keyword

hard,more,nonn

Author

Jonathan Vos Post, Feb 07 2006

Extensions

8 more terms from R. J. Mathar, Oct 20 2013

Status

approved