A001672
a(n) = floor(Pi^n).
Original entry on oeis.org
1, 3, 9, 31, 97, 306, 961, 3020, 9488, 29809, 93648, 294204, 924269, 2903677, 9122171, 28658145, 90032220, 282844563, 888582403, 2791563949, 8769956796, 27551631842, 86556004191, 271923706893, 854273519913, 2683779414317, 8431341691876, 26487841119103
Offset: 0
See also
A002160: closest integer to Pi^n.
A002160
Nearest integer to Pi^n.
Original entry on oeis.org
1, 3, 10, 31, 97, 306, 961, 3020, 9489, 29809, 93648, 294204, 924269, 2903677, 9122171, 28658146, 90032221, 282844564, 888582403, 2791563950, 8769956796, 27551631843, 86556004192, 271923706894, 854273519914, 2683779414318, 8431341691876, 26487841119104, 83214007069230
Offset: 0
a(0) = 1 because Pi^0 = 1;
a(2) = 10 because Pi^2 = 9.8696...;
a(10) = 93648 because Pi^10 = 93648.047476...
- 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.
- J. T. Peters, Ten-Place Logarithm Table. Vols. 1 and 2, rev. ed. Ungar, NY, 1957, Vol. 1 (Appendix), p. 1.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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a := []: Digits := 1000: for n from 0 to 50 do: a := [op(a),round(Pi^n)]: od: seq(a[i+1],i=0..50);
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Round[Pi^Range[0,40]] (* Harvey P. Dale, Jun 10 2024 *)
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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
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[round(pi^n) for n in range(0,29)] # Stefano Spezia, Jan 15 2025
More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003
A111937
Integers k such that ceiling(Pi^k) is prime.
Original entry on oeis.org
5, 29, 88, 948, 1071, 1100, 1578, 14357
Offset: 1
a(1)=5: ceiling(3.14159265...^5) = ceiling(306.0196847...) = 307, which is prime.
- Eric Weisstein's World of Mathematics, Phi-Prime
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$MaxExtraPrecision = 2^20; Do[ If[ PrimeQ[ Ceiling[Pi^n]], Print[n]], {n, 10000}] (* Robert G. Wilson v, Nov 28 2005 *)
A118843
Primes of the form ceiling(Pi^k).
Original entry on oeis.org
307, 261424513284461, 56129192858827520816193436882886842322337671
Offset: 1
Showing 1-4 of 4 results.
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