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%I #16 Nov 08 2020 03:01:01
%S 1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,8,9,9,9,10,10,10,11,
%T 11,11,12,12,12,13,13,13,14,14,14,15,15,15,15,16,16,16,17,17,17,18,18,
%U 18,19,19,19,20,20,20,21,21,21,22,22,22,22,23,23,23,24,24,24,25,25,25,26,26,26,27,27
%N a(n) = ceiling of n/Pi.
%C The problem asks if a(n) is also equal to ceiling(cosec(Pi/n)) for n>3.
%C First differs from ceiling(cosec(Pi/n)) for n>3 at n=80143857 (Stadler, 2019; Velleman and Wagon, 2020). - _Amiram Eldar_, Nov 08 2020
%D Daniel J. Velleman and Stan Wagon, Bicycle or Unicycle?, MAA Press, 2020, pp. 32 and 192-194.
%H Jonathan D. Lee and Stan Wagon, Proposers, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.124.10.970">Problem 12006</a>, The American Mathematical Monthly, Vol. 124, No. 10 (2017), p. 970.
%H Albert Stadler and others, <a href="https://doi.org/10.1080/00029890.2019.1583529">A Suspicious Formula Involving Pi</a>, solution to Problem 12006, The American Mathematical Monthly, Vol. 126, No. 5 (2019), pp. 475-476.
%t a[n_] := Ceiling[n/Pi]; Array[a, 100] (* _Amiram Eldar_, Nov 08 2020 *)
%o (PARI) a(n)=n\Pi+1 \\ _Charles R Greathouse IV_, Mar 04 2018
%Y Cf. A032615.
%K nonn
%O 1,4
%A _N. J. A. Sloane_, Dec 15 2017