A347029 a(n) = ceiling(e^(n*(Pi/2))).

1, 5, 24, 112, 536, 2576, 12392, 59610, 286752, 1379411, 6635624, 31920520, 153552936, 738662923, 3553321281, 17093171649, 82226315586, 395547831245, 1902773895293, 9153250784395, 44031505860633, 211812562992414, 1018919543279305, 4901489415968643, 23578503968558227

Offset: 0

Author

Gary W. Adamson, Aug 11 2021

Keywords

• nonn

Comments

Alternative formula for e^(n*Pi/2) is i^(-n*i), where i = sqrt(-1). Substitute 2i for n in each identity, resulting in e^(Pi*i) = -1; Euler's formula.

A121905 is the bisection of the sequence, ceiling(e^(n*Pi)).

Examples

			a(5) = ceiling(e^(5*Pi/2)) = ceiling(i^(-5*i)) = 2576.
		

Crossrefs

Cf. A121905 (even bisection), A124507 (floor), A042972.

Programs

Mathematica

a[n_]:=Ceiling[Exp[n Pi/2]]; Table[a[n],{n,0,24}] (* Stefano Spezia, Aug 12 2021 *)

PARI

a(n) = ceil(exp(n*Pi/2)); \\ Michel Marcus, Aug 12 2021

Formula

a(n) = ceiling(e^(n*Pi/2)) = ceiling(i^(-n*i)).