A114333 Integers K with prime sum of the first K factorials of odd numbers.

2, 3, 4, 5, 28, 32

Offset: 1

Author

Jonathan Vos Post, Feb 06 2006

Keywords

• nonn
• fini
• full

Comments

k = 6, 7, 8, 22, 27, and 29 yield semiprimes.

The sequence is finite because the sum of the factorials of the first k odd numbers is divisible by 107 for every k >= 53. - Giovanni Resta, Jun 14 2016

Examples

			a(1) = 2 because 1! + 3! = 7 is prime.
a(2) = 3 because 1! + 3! + 5! = 127 is prime.
a(3) = 4 because 1! + 3! + 5! + 7! = 5167 is prime.
a(5) = 28 because 1! + 3! + 5! + 7! + 9! + 11! + 13! + 15! + 17! + 19! + 21! + 23! + 25! + 27! + 29! + 31! + 33! + 35! + 37! + 39! + 41! + 43! + 45! + 47! + 49! + 51! + 53! + 55! = 12700679788669629845870127416097655693745481645117320232505943379392681647 is prime.
a(6) = 32 because 1! + 3! + ... + (2*32+1)! = 1! + 3! + ... + 63! = 1983116034341975454789449189498620955194254460449807567074683265838922666583379392681647 is prime.
		

Crossrefs

Cf. A000040, A000142, A005408.

Programs

Mathematica

Select[Range[100], PrimeQ[Sum[(2 k - 1)!, {k, #}]] &] (* Giovanni Resta, Jun 14 2016 *)

Formula

{a(n)} = {k such that 1! + 3! + ... + (2k-1)! is prime}.

{a(n)} = {k such that Sum_{j=1..k} A000142(A005408(j)) is in A000040}.

Extensions

Missing a(4) = 5 and keywords fini and full added by Giovanni Resta, Jun 14 2016