%I M2841 N1142 #24 Jun 10 2024 17:21:05

%S 1,3,10,31,97,306,961,3020,9489,29809,93648,294204,924269,2903677,

%T 9122171,28658146,90032221,282844564,888582403,2791563950,8769956796,

%U 27551631843,86556004192,271923706894,854273519914,2683779414318,8431341691876,26487841119104,83214007069230

%N Nearest integer to Pi^n.

%D A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 122.

%D J. T. Peters, Ten-Place Logarithm Table. Vols. 1 and 2, rev. ed. Ungar, NY, 1957, Vol. 1 (Appendix), p. 1.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%e a(0) = 1 because Pi^0 = 1;

%e a(2) = 10 because Pi^2 = 9.8696...;

%e a(10) = 93648 because Pi^10 = 93648.047476...

%p a := []: Digits := 1000: for n from 0 to 50 do: a := [op(a),round(Pi^n)]: od: seq(a[i+1],i=0..50);

%t Round[Pi^Range[0,40]] (* _Harvey P. Dale_, Jun 10 2024 *)

%o (PARI) apply( A002160(n)=Pi^n\/1, [0..50]) \\ An error message will say so if default(realprecision) must be increased. - _M. F. Hasler_, May 27 2018

%Y Cf. A000227 (e^n), A001672 (floor(Pi^n)), A001673 (ceiling(Pi^n)).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003

%E Edited by _M. F. Hasler_, May 27 2018