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 A214839 Ratios of consecutive terms approach Pi alternating from below and above. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Eric M. Schmidt, Table of n, a(n) for n = 1..2000 EXAMPLE a(2) = 3 since 3/1 < Pi, while 4/1 > Pi. a(3) = 10 since 10/3 > Pi, while 9/3 < Pi. MATHEMATICA 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]]] PROG (Sage) def A214839(numterms) :     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 # Eric M. Schmidt, Mar 26 2013 CROSSREFS Sequence in context: A068094 A100058 A002160 * A114487 A017934 A005510 Adjacent sequences:  A214836 A214837 A214838 * A214840 A214841 A214842 KEYWORD easy,nonn AUTHOR William J. Keith, Mar 08 2013 STATUS approved

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Last modified August 3 19:05 EDT 2021. Contains 346441 sequences. (Running on oeis4.)