

A076539


Numerators a(n) of fractions slowly converging to Pi: let a(1) = 0, b(n) = n  a(n); if (a(n) + 1) / b(n) < pi, then a(n+1) = a(n) + 1, else a(n+1)= a(n).


1



0, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 52, 53, 53, 54, 55
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OFFSET

1,3


COMMENTS

a(n) + b(n) = n and as n > +infinity, a(n) / b(n) converges to Pi. For all n, a(n) / b(n) < Pi.


LINKS

Table of n, a(n) for n=1..73.


FORMULA

a(1) = 0, b(n) = n  a(n), if (a(n) + 1) / b(n) < pi, then a(n+1) = a(n) + 1, else a(n+1) = a(n).
a(n) = floor(n*Pi/(Pi+1)).  Vladeta Jovovic, Oct 04 2003


EXAMPLE

a(7)= 5 so b(7) = 7  5 = 2. a(8) = 6 because (a(7) + 1) / b(7) = 6/2 which is < Pi. So b(8) = 8  6 = 2. a(9) = 6 because (a(8) + 1) / b(8) = 7/2 which is not < Pi.


MATHEMATICA

Array[Floor[# Pi/(Pi + 1)] &, 73] (* Michael De Vlieger, Jan 11 2018 *)


CROSSREFS

Cf. A074840, A074065, A060143.
Sequence in context: A215090 A083544 A057353 * A074184 A187329 A093700
Adjacent sequences: A076536 A076537 A076538 * A076540 A076541 A076542


KEYWORD

easy,frac,nonn


AUTHOR

Robert A. Stump (bee_ess107(AT)msn.com), Oct 18 2002


STATUS

approved



