

A284123


Numbers n such that A099953(n) = Sum_{i=1..n1} (2i1)!! is prime.


0




OFFSET

1,1


COMMENTS

The first 3 associated primes are 19, 1069, 8236528396549. The next 3 terms are about 3.739... * 10^990, 2.378... * 10^1196 and 1.059... * 10^1262.
The sequence contains primes in the partial sums of (2n1)!!. The corresponding primes in the partial sums of (2n)!! is the finite sequence A283563. Is this sequence also finite?
If for some n, (2n1)a(n) then a(k) is divisible by (2n1) (and thus composite) for all k > n.


LINKS

Table of n, a(n) for n=1..7.


EXAMPLE

6 is in this sequence because 1!! + 3!! + 5!! + 7!! + 9!! = 1 + 1*3 + 1*3*5 + 1*3*5*7 + 1*3*5*7*9 = 1069 is prime. In general, n is in this sequence if 1!! + 3!! + 5!! + ... + (2n3)!! is prime.


MATHEMATICA

a[n_] := Sum[(2 i  1)!!, {i, 1, n  1}]; Select[Range[0, 500], PrimeQ[a[#]] &]


CROSSREFS

Cf. A099953, A283563.
Sequence in context: A096003 A114058 A214901 * A135093 A141667 A048753
Adjacent sequences: A284120 A284121 A284122 * A284124 A284125 A284126


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Mar 22 2017


EXTENSIONS

a(7) from Vaclav Kotesovec, Mar 28 2017


STATUS

approved



