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A076539
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Numerators a(n) of fractions slowly converging to Pi: let a(1) = 0, b(n) = n - a(n); if (a(n) + 1) / b(n) < pi, then a(n+1) = a(n) + 1, else a(n+1)= a(n).
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1
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0, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 52, 53, 53, 54, 55
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) + b(n) = n and as n -> +infinity, a(n) / b(n) converges to Pi. For all n, a(n) / b(n) < Pi.
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FORMULA
| a(1) = 0, b(n) = n - a(n), if (a(n) + 1) / b(n) < pi, then a(n+1) = a(n) + 1, else a(n+1) = a(n).
a(n) = floor(n*Pi/(Pi+1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 04 2003
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EXAMPLE
| a(7)= 5 so b(7) = 7 - 5 = 2. a(8) = 6 because (a(7) + 1) / b(7) = 6/2 which is < Pi. So b(8) = 8 - 6 = 2. a(9) = 6 because (a(8) + 1) / b(8) = 7/2 which is not < Pi.
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CROSSREFS
| Cf. A074840, A074065, A005206.
Sequence in context: A120503 A083544 A057353 * A074184 A187329 A093700
Adjacent sequences: A076536 A076537 A076538 * A076540 A076541 A076542
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KEYWORD
| easy,frac,nonn
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AUTHOR
| Robert A. Stump (bee_ess107(AT)msn.com), Oct 18 2002
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