A138324 a(n) = the second term in the simple continued fraction of Pi^n.

7, 1, 159, 2, 50, 2, 3, 1, 10, 21, 55, 5, 3, 5, 1, 1, 1, 14, 1, 12, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1, 1, 11, 2, 1, 1, 3, 3, 1, 1, 1, 2, 1, 1, 1, 7, 1, 8, 1, 2, 33, 1, 1, 1, 1, 117, 1, 2, 1, 1, 1, 8, 1, 2, 1, 1, 1, 1, 1, 27, 1, 1, 5, 4, 1, 1, 1, 270, 1, 1, 1, 5, 3, 1, 25, 2, 10, 9, 1, 16, 1, 1, 1

Offset: 1

Author

Leroy Quet, Mar 14 2008

Keywords

• nonn

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001672.

Programs

Mathematica

Table[Floor[1/(# - Floor[#])] &[Pi^n], {n, 96}] (* Michael De Vlieger, Aug 29 2017 *)

PARI

\p 2000 a(n) = floor(1/(Pi^n - floor(Pi^n))); for(i=1,100,print1(a(i),",")) \\ Vim Wenders, Mar 28 2008

Formula

a(n) = floor(1/(pi^n - floor(pi^n))).

Extensions

More terms from Vim Wenders, Mar 28 2008