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A156020
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Denominators in an infinite sum for Pi.
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3
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1, 106, 877203, 2195225334, 17599271777, 360950005720, 17348726394920, 1996375977735378, 26627865341803449, 668044491303666717, 13157161331655387213, 7653283960850915182425, 3256741424583567733172850, 388712386741794886666062286, 266182386623377135274423955447
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OFFSET
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1,2
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COMMENTS
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For k >= 0, define Q(k) = A002485(2k)/A002486(2k) (convergents to Pi that are less than Pi), so Pi = Sum_{k>=1} (Q(k) - Q(k-1)). Then a(n) is the denominator of Q(n) - Q(n-1).
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LINKS
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FORMULA
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EXAMPLE
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Pi = 3/1 + 15/106 + 73/877203 + 1/2195225334 + 2/17599271777 + 3/360950005720 + 7/17348726394920 + ....
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- ------------------------------ ------------- ------
0 0/1 = 0 - -
1 3/1 = 3 3/1 1
2 333/106 = 3.1415094339... 15/106 106
3 103993/33102 = 3.1415926530... 73/877203 877203
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PROG
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(PARI) cfPi=contfrac(Pi);
vA002485 = concat(1, contfracpnqn(cfPi, #cfPi)[1, ]);
A002486(n) = contfracpnqn(vecextract(cfPi, 2^n-1))[2, 2];
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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