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A340066
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Decimal expansion of the Product_{p>=3} 1+p^2/((p-1)^2*(p+1)^2) where p are successive prime numbers A000040.
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1
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1, 2, 5, 3, 6, 1, 7, 9, 4, 5, 0, 0, 7, 2, 3, 5, 8, 9, 0, 0, 1, 4, 4, 7, 1, 7, 8, 0, 0, 2, 8, 9, 4, 3, 5, 6, 0, 0, 5, 7, 8, 8, 7, 1, 2, 0, 1, 1, 5, 7, 7, 4, 2, 4, 0, 2, 3, 1, 5, 4, 8, 4, 8, 0, 4, 6, 3, 0, 9, 6, 9, 6, 0, 9, 2, 6, 1, 9, 3, 9, 2, 1, 8, 5, 2, 3, 8, 7, 8, 4, 3, 7, 0, 4, 7, 7, 5, 6, 8, 7, 4, 0, 9, 5, 5
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OFFSET
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1,2
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COMMENTS
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This is a rational number.
This constant does not belong to the infinite series of prime number products of the form: Product_{p>=2} (p^(2*n)-1)/(p^(2*n)+1),
which are rational numbers equal to zeta(4*n)/zeta^2(2*n) = A114362(n+1)/A114363(n+1).
This number has decimal period length 230:
1.25(3617945007235890014471780028943560057887120115774240231548480463096960
9261939218523878437047756874095513748191027496382054992764109985528219
9710564399421128798842257597684515195369030390738060781476121562952243
12590448625180897250).
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LINKS
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Table of n, a(n) for n=1..105.
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FORMULA
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Equals 3465/2764 = 3^2*5*7*11/(2^2*691).
Equals Product_{n>=2} 1+A000040(n)^2/A084920(n)^2.
Equals (9/13)*A340065.
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EXAMPLE
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1.25361794500723589001447178...
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MATHEMATICA
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RealDigits[N[3465/2764, 105]][[1]]
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PROG
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(PARI)
default(realprecision, 105)
prodeulerrat(1+p^2/((p-1)^2*(p+1)^2), 1, 3)
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CROSSREFS
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Cf. A065483, A065484, A065485, A109695, A111003, A114362, A114363, A116393, A167864, A231535, A307868, A330523, A330595, A335319, A335762, A335818, A339925, A340065.
Sequence in context: A085825 A198140 A339259 * A212614 A037852 A226214
Adjacent sequences: A340063 A340064 A340065 * A340067 A340068 A340069
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KEYWORD
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nonn,cons
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AUTHOR
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Artur Jasinski, Dec 28 2020
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STATUS
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approved
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