A284123 Numbers n such that A099953(n) = Sum_{i=1..n-1} (2i-1)!! is prime.

4, 6, 14, 402, 472, 494, 7926, 13060

Offset: 1

Author

Amiram Eldar, Mar 22 2017

Keywords

• nonn
• more

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 (2n-1)!!. The corresponding primes in the partial sums of (2n)!! is the finite sequence A283563. Is this sequence also finite?

If for some n, (2n-1)|a(n) then a(k) is divisible by (2n-1) (and thus composite) for all k > n.

Examples

			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!! + ... + (2n-3)!! is prime.
		

Crossrefs

Cf. A099953, A283563.

Programs

Mathematica

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

Extensions

a(7) from Vaclav Kotesovec, Mar 28 2017

a(8) from Michael S. Branicky, Sep 26 2024