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

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

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