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A286742
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a(n) minimizes (over the integers) the absolute difference between Pi and x(n) + 1/a(n), where x(n) is Pi truncated at the n-th decimal digit.
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0
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7, 24, 628, 1687, 10793, 376848, 1530012, 18660270, 278567575, 1695509434, 11136696004, 102111268282, 1260654956982, 10725187563686, 308788493220130, 4193528956200936, 25999253094360135, 118166387818704585, 2161492060929047665, 15963377896404315144
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OFFSET
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1,1
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LINKS
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EXAMPLE
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3 + 1/7 is closest to Pi in absolute value among numbers of the form 3 + 1/k (k an integer); 3.1 + 1/24 is closest to Pi in absolute value among numbers of the form 3.1 + 1/k (k an integer); 3.14 + 1/628 is closest to Pi in absolute value among numbers of the form 3.14 + 1/k (k an integer).
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MATHEMATICA
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Table[
truncpi = Floor[10^(n - 1)*Pi]/10^(n - 1);
SortBy[
{Floor[1/(Pi - truncpi)], Ceiling[1/(Pi - truncpi)]},
N[Abs[Pi - (truncpi + 1/#)]] &
][[1]],
{n, 1, 20}] (* first 20 terms *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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