1,1

k = 6, 7, 8, 29 yield semiprimes.

{a(n)} = {k such that 1! + 3! + ... + (2k-1)! is prime}. {a(n)} = (k such that SUM[from j=1 to k] A000142(A005408(j)) is in A000040}.

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(4) = 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(5) = 32 because 1! + 3! + ... + (2*32+1)! = 1! + 3! + ... + 63! = 1983116034341975454789449189498620955194254460449807567074683265838922666583379392681647 is prime.

Cf. A000040, A000142, A005408.

Sequence in context: A098549 A100604 A062931 this_sequence A059614 A028426 A024633

Adjacent sequences: A114330 A114331 A114332 this_sequence A114334 A114335 A114336

nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 06 2006