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A214839
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Ratios of consecutive terms approach Pi alternating from below and above.
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1
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1, 3, 10, 31, 98, 307, 965, 3031, 9523, 29917, 93988, 295272, 927625, 2914219, 9155290, 28762191, 90359088, 283871447, 891808453, 2801698884, 8801796632, 27651659637, 86870250776, 272910941653, 857375009382, 2693523030845, 8461952165978, 26584006759664
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OFFSET
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1,2
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COMMENTS
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The alternation of ratios above and below is chosen to match the behavior of ratios of the Fibonacci numbers with respect to the golden ratio.
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LINKS
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EXAMPLE
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a(2) = 3 since 3/1 < Pi, while 4/1 > Pi. a(3) = 10 since 10/3 > Pi, while 9/3 < Pi.
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MATHEMATICA
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PiApprox = Table[1, {i, 1, 40}]; For[i = 2, i < 41, i++, If[Mod[i, 2] == 0, PiApprox[[i]] = Floor[PiApprox[[i - 1]]*Pi], PiApprox[[i]] = Ceiling[PiApprox[[i - 1]]*Pi]]]
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PROG
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(Sage)
res = [1]
for i in range(1, numterms) :
res.append(floor(pi*res[i-1]) if is_odd(i) else ceil(pi*res[i-1]))
return res
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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