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A181055
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Numbers n such that sum_{k=1..n} (-1)^(n-k) *bigomega(k) is prime.
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0
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4, 6, 8, 10, 12, 24, 26, 28, 30, 32, 34, 46, 52, 70, 78, 82, 102, 126, 128, 132, 134, 136, 138, 168, 186, 190, 192, 222, 234, 274, 280, 312, 316, 322, 336, 378, 418, 424, 426, 440, 472, 484, 492, 504, 532, 540, 558, 570, 574, 584, 592, 602, 604, 606, 650, 652
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OFFSET
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1,1
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COMMENTS
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The partial alternating sum over bigomega(.)=A001222(.) in the definition starts at n=1
as 0, 1, 0, 2, -1, 3, -2, 5, -3, 5, -4, 7, -6, 8 ...
The first primes in this signed sequence are
2, 3, 5, 5, 7, 17, 17, 17, 19, 23, 23, 31, 37, 53, 59, 61, 79, 97, 103, 107, 107, 107, 109,...
occurring at positions 4, 6, 8, 10 etc, which define the sequence.
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LINKS
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EXAMPLE
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6 is in the sequence because sum_{k=1..6}(-1)^ (6-k)*bigomega(k) =
((-1)^5)*0 + ((-1)^4)*1 + ((-1)^3)*1 + ((-1)^2)*2 + ((-1)^1)*1 + ((-1)^0)*2 =
0 + 1 -1 + 2 -1 + 2 = 3 is prime.
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MAPLE
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with(numtheory):for n from 1 to 1000 do: s:=0: for k from 1 to n do :s:=s+((-1)^(n-k))*bigomega(k):od: if type(s, prime)=true then printf(`%d, `, n):else fi:od:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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