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A114333
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Integers K with prime sum of the first K factorials of odd numbers.
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1
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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{a(n)} = {k such that 1! + 3! + ... + (2k-1)! is prime}.
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[100], PrimeQ[Sum[(2 k - 1)!, {k, #}]] &] (* Giovanni Resta, Jun 14 2016 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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Missing a(4) = 5 and keywords fini and full added by Giovanni Resta, Jun 14 2016
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STATUS
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approved
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