A296357 a(n) = ceiling of n/Pi.

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, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 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

Offset: 1

Author

N. J. A. Sloane, Dec 15 2017

Keywords

• nonn

Comments

The problem asks if a(n) is also equal to ceiling(cosec(Pi/n)) for n>3.

First differs from ceiling(cosec(Pi/n)) for n>3 at n=80143857 (Stadler, 2019; Velleman and Wagon, 2020). - Amiram Eldar, Nov 08 2020

References

• Daniel J. Velleman and Stan Wagon, Bicycle or Unicycle?, MAA Press, 2020, pp. 32 and 192-194.

Links

• Jonathan D. Lee and Stan Wagon, Proposers, Problem 12006, The American Mathematical Monthly, Vol. 124, No. 10 (2017), p. 970.
• Albert Stadler and others, A Suspicious Formula Involving Pi, solution to Problem 12006, The American Mathematical Monthly, Vol. 126, No. 5 (2019), pp. 475-476.

Crossrefs

Cf. A032615.

Programs

Mathematica

a[n_] := Ceiling[n/Pi]; Array[a, 100] (* Amiram Eldar, Nov 08 2020 *)

PARI

a(n)=n\Pi+1 \\ Charles R Greathouse IV, Mar 04 2018