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A214839 Ratios of consecutive terms approach Pi alternating from below and above. 1

%I

%S 1,3,10,31,98,307,965,3031,9523,29917,93988,295272,927625,2914219,

%T 9155290,28762191,90359088,283871447,891808453,2801698884,8801796632,

%U 27651659637,86870250776,272910941653,857375009382,2693523030845,8461952165978,26584006759664

%N Ratios of consecutive terms approach Pi alternating from below and above.

%C 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.

%H Eric M. Schmidt, <a href="/A214839/b214839.txt">Table of n, a(n) for n = 1..2000</a>

%e a(2) = 3 since 3/1 < Pi, while 4/1 > Pi. a(3) = 10 since 10/3 > Pi, while 9/3 < Pi.

%t 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]]]

%o (Sage)

%o def A214839(numterms) :

%o res = [1]

%o for i in range(1, numterms) :

%o res.append(floor(pi*res[i-1]) if is_odd(i) else ceil(pi*res[i-1]))

%o return res

%o # _Eric M. Schmidt_, Mar 26 2013

%K easy,nonn

%O 1,2

%A _William J. Keith_, Mar 08 2013

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Last modified June 1 04:37 EDT 2020. Contains 334758 sequences. (Running on oeis4.)