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Search: id:A073579
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| A073579 |
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Signed primes: if prime(n) even, a(n) = 0; if prime(i) == 1 (mod 4), a(i)=prime(i); if prime(i) == -1 (mod 4), a(i)=-prime(i). |
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+0
4
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| 0, -3, 5, -7, -11, 13, 17, -19, -23, 29, -31, 37, 41, -43, -47, 53, -59, 61, -67, -71, 73, -79, -83, 89, 97, 101, -103, -107, 109, 113, -127, -131, 137, -139, 149, -151, 157, -163, -167, 173, 179, 181, -191, 193, 197, -199, -211, -223, -227, 229, 233, -239, 241, -251, 257, -263, 269, -271, 277, 281
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Product(i>1)(1/(1-1/a(i))) = 1-1/3+1/5-1/7-1/9+1/11... = pi/4 Product(i>1)(1/(1+1/a(i))) = pi/2 Product(i>1)(1/(1-1/a(i)))*Product(i>1)(1/(1+1/a(i))) = Product(i>1)(1/(1-1/P(i)^2)) = 1+1/3^2+1/5^2+1/7^2+1/9^2+... = pi^2/8
Also prime(n)*(2 - prime(n) mod 4) = A000040(n)*A070750(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Oct 21 2002
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FORMULA
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a(1)=0, and for i>1: a(i)=(-1)^((prime(i)-1)/2)*prime(i)
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EXAMPLE
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a(1)=0 because prime(1)=2 neither 4k+1, nor 4k-1. a(6)=13=prime(6) because 13=4*3+1 a(8)=-19=-prime(8) because 19=4*5-1
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CROSSREFS
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Cf. A000040.
Sequence in context: A074918 A006005 A065091 this_sequence A065380 A038134 A138980
Adjacent sequences: A073576 A073577 A073578 this_sequence A073580 A073581 A073582
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KEYWORD
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easy,sign
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Aug 28 2002
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