%I A114333
%S A114333 2,3,4,28,32
%N A114333 Integers K with prime sum of the first K factorials of odd numbers.
%C A114333 k = 6, 7, 8, 29 yield semiprimes.
%F A114333 {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}.
%e A114333 a(1) = 2 because 1! + 3! = 7 is prime.
%e A114333 a(2) = 3 because 1! + 3! + 5! = 127 is prime.
%e A114333 a(3) = 4 because 1! + 3! + 5! + 7! = 5167 is prime.
%e A114333 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! = 1270067978866962984587012741609765569374548164511732023250594\
               3379392681647 is prime.
%e A114333 a(5) = 32 because 1! + 3! + ... + (2*32+1)! = 1! + 3! + ... + 63! = 19831160343419754547894491894986209551942\
               54460449807567074683265838922666583379392681647 is prime.
%Y A114333 Cf. A000040, A000142, A005408.
%Y A114333 Sequence in context: A098549 A100604 A062931 this_sequence A059614 A028426 
               A024633
%Y A114333 Adjacent sequences: A114330 A114331 A114332 this_sequence A114334 A114335 
               A114336
%K A114333 nonn
%O A114333 1,1
%A A114333 Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 06 2006