cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Keywords

Crossrefs

See also A002160: closest integer to Pi^n.
Cf. A001673.

Programs

Formula

a(n)^(1/n) converges to Pi because |1 - a(n)/Pi^n| = |Pi^n - a(n)|/Pi^n < 1/Pi^n and so a(n)^(1/n) = (Pi^n*(1+o(1)))^(1/n) = Pi*(1+o(1)). - Hieronymus Fischer, Jan 22 2006

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

Views

Author

Keywords

Examples

			a(0) = 1 because Pi^0 = 1;
a(2) = 10 because Pi^2 = 9.8696...;
a(10) = 93648 because Pi^10 = 93648.047476...
		

References

  • 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).

Crossrefs

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

Programs

  • Maple
    a := []: Digits := 1000: for n from 0 to 50 do: a := [op(a),round(Pi^n)]: od: seq(a[i+1],i=0..50);
  • Mathematica
    Round[Pi^Range[0,40]] (* Harvey P. Dale, Jun 10 2024 *)
  • 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
    
  • Sage
    [round(pi^n) for n in range(0,29)] # Stefano Spezia, Jan 15 2025

Extensions

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003
Edited by M. F. Hasler, May 27 2018

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

Views

Author

Ray G. Opao, Nov 27 2005

Keywords

Examples

			a(1)=5: ceiling(3.14159265...^5) = ceiling(306.0196847...) = 307, which is prime.
		

Crossrefs

Cf. A001673.

Programs

  • Mathematica
    $MaxExtraPrecision = 2^20; Do[ If[ PrimeQ[ Ceiling[Pi^n]], Print[n]], {n, 10000}] (* Robert G. Wilson v, Nov 28 2005 *)

Extensions

a(5)-a(7) from Robert G. Wilson v, Nov 28 2005
a(8) from Donovan Johnson, Feb 04 2008

A118843 Primes of the form ceiling(Pi^k).

Original entry on oeis.org

307, 261424513284461, 56129192858827520816193436882886842322337671
Offset: 1

Views

Author

Eric W. Weisstein, May 01 2006

Keywords

Comments

The next term (a(4)) has 472 digits. - Harvey P. Dale, Jan 16 2023

Crossrefs

Programs

  • Mathematica
    Select[Ceiling[Pi^Range[0,100]],PrimeQ] (* Harvey P. Dale, Jan 16 2023 *)
Showing 1-4 of 4 results.