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.

A102475 a(n) = floor(Pi^(n/2)).

Original entry on oeis.org

1, 1, 3, 5, 9, 17, 31, 54, 97, 172, 306, 542, 961, 1704, 3020, 5353, 9488, 16817, 29809, 52835, 93648, 165986, 294204, 521463, 924269, 1638224, 2903677, 5146633, 9122171, 16168627, 28658145, 50795241, 90032220, 159577956, 282844563, 501328935, 888582403
Offset: 0

Views

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 24 2005

Keywords

Crossrefs

Programs

  • Mathematica
    Floor[Pi^(Range[0,40]/2)] (* Harvey P. Dale, Aug 27 2012 *)

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 27 2019

A212463 a(n) = ceiling( Pi^(n/3) ).

Original entry on oeis.org

2, 3, 4, 5, 7, 10, 15, 22, 32, 46, 67, 98, 143, 209, 307, 449, 657, 962, 1409, 2063, 3021, 4424, 6479, 9489, 13897, 20354, 29810, 43659, 63942, 93649, 137157, 200878, 294205, 430889, 631077, 924270, 1353678
Offset: 1

Views

Author

Mohammad K. Azarian, Jul 02 2012

Keywords

Crossrefs

Programs

  • Derive
    PROG(y := [], n := 60, LOOP(IF(n = 0, RETURN y), y := ADJOIN(CEILING((pi)^(n/3)), y), n := n - 1))
    
  • Mathematica
    a[n_]:= Ceiling[((Pi)^(n/3))]; Table[a[n], {n, 1, 50}] (* Vincenzo Librandi, Feb 14 2013 *)
  • PARI
    a(n) = ceil(Pi^(n/3)); \\ Michel Marcus, Jan 11 2016

A212464 a(n) = floor( Pi^(n/3) ).

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 14, 21, 31, 45, 66, 97, 142, 208, 306, 448, 656, 961, 1408, 2062, 3020, 4423, 6478, 9488, 13896, 20353, 29809, 43658, 63941, 93648, 137156, 200877, 294204, 430888, 631076, 924269, 1353677
Offset: 1

Views

Author

Mohammad K. Azarian, Jul 02 2012

Keywords

Crossrefs

Programs

  • Derive
    PROG(y := [], n := 60, LOOP(IF(n = 0, RETURN y), y := ADJOIN(floor((pi)^(n/3)), y), n := n - 1))
    
  • Maple
    A212464:=n->floor(Pi^(n/3)): seq(A212464(n), n=1..60); # Wesley Ivan Hurt, Feb 09 2017
  • Mathematica
    a[n_]:= Floor[((Pi)^(n/3))]; Table[a[n], {n, 1, 60}] (* Vincenzo Librandi, Feb 14 2013 *)
  • PARI
    a(n) = floor(Pi^(n/3)); \\ Michel Marcus, Jan 11 2016

A306604 Number of perfect squares in the half-open interval [Pi^(n-1), Pi^n).

Original entry on oeis.org

0, 1, 2, 2, 4, 8, 14, 23, 43, 75, 134, 236, 419, 743, 1316, 2333, 4135, 7329, 12992, 23026, 40813, 72338, 128218, 227259, 402806, 713955, 1265453, 2242956, 3975538, 7046456, 12489518, 22137096, 39236979, 69545736, 123266607, 218484372, 387253468, 686388899
Offset: 0

Views

Author

Alois P. Heinz, Feb 27 2019

Keywords

Comments

Inspired by A306486.

Examples

			a(4) = 4: in the interval [Pi^3, Pi^4) = [31.006..., 97.409...) = are four perfect squares: 36, 49, 64, 81.
		

Crossrefs

Programs

  • Maple
    a:= n-> (f-> f(n)-f(n-1))(i-> ceil(Pi^(i/2))):
    seq(a(n), n=0..42);

Formula

a(n) = ceiling(Pi^(n/2)) - ceiling(Pi^((n-1)/2)).
a(n) = A102477(n) - A102477(n-1).
Sum_{i=0..n} a(i) = A102475(n) for n > 0.
Lim_{n->oo} a(n+1)/a(n) = sqrt(Pi) = 1.7724538509... = A002161.
Showing 1-4 of 4 results.