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A284123 Numbers n such that A099953(n) = Sum_{i=1..n-1} (2i-1)!! is prime. 0
4, 6, 14, 402, 472, 494, 7926 (list; graph; refs; listen; history; text; internal format)
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 (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.

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

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Last modified August 5 06:46 EDT 2020. Contains 336209 sequences. (Running on oeis4.)