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 1-7 of 7 results.

A067100 Floor[radius of the inscribed-circle of a regular n-gon with unit sides].

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11
Offset: 3

Views

Author

Amarnath Murthy, Jan 07 2002

Keywords

Examples

			a(24) = floor(cot(Pi/24)/2) = floor(3.79787705636257522026320957021073) = 3.

Links

Crossrefs

Cf. A067099, A062299.

Programs

  • Mathematica
    Table[ Floor[ Cot[Pi/n]/2], {n, 3, 75} ]
  • PARI
    { for (n=3, 1000, write("b067100.txt", n, " ", floor((cotan(Pi/n)/2))) ) } \\ Harry J. Smith, May 19 2010

Formula

a(n) = floor((cot(Pi/n)/2)).

Extensions

More terms from Robert G. Wilson v, Jan 09 2002

A067101 Floor[ X/Y], where X = concatenation of the primes and Y = concatenation of natural numbers.

Original entry on oeis.org

2, 1, 1, 1, 19, 190, 1909, 19092, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 1909260, 19092601, 190926018, 1909260182, 19092601827, 190926018273
Offset: 1

Views

Author

Amarnath Murthy, Jan 07 2002

Keywords

Examples

			a(5) = floor [235711/12345]=floor[19.093641150...] = 19.

Crossrefs

Cf. A067091, A067092, A067093, A067094, A067095, A067096, A067097, A067098, A067099.
floor[A019518(n)/A007908(n)]

Programs

  • Mathematica
    f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[Prime[k]]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 25} ]
nn=40;With[{prs=Prime[Range[nn]],nats=Range[nn]},Table[Floor[FromDigits[ Flatten[IntegerDigits/@Take[prs,n]]]/FromDigits[Flatten[IntegerDigits /@Take[nats,n]]]],{n,nn}]] (* Harvey P. Dale, Mar 24 2012 *)

Extensions

More terms from Robert G. Wilson v, Jan 09 2002

A067102 Floor[ X/Y] where X = concatenation of the squares and Y = concatenation of natural numbers.

Original entry on oeis.org

1, 1, 1, 12, 120, 1208, 12082, 120821, 1208216, 12082165, 120821655, 1208216555, 12082165556, 120821655562, 1208216555626, 12082165556267, 120821655562672, 1208216555626728, 12082165556267282, 120821655562672822
Offset: 1

Views

Author

Amarnath Murthy, Jan 07 2002

Keywords

Examples

			a(5) = floor [1491625/12345]=floor[] = floor[120.828270554880518428513568246254]=120.

Crossrefs

Cf. A067091, A067092, A067093, A067094, A067095, A067096, A067097, A067098, A067099, A067100, A067101.
floor[A019521(n)/A007908(n)]

Programs

  • Mathematica
    f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[k^2]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 20} ]

Extensions

More terms from Robert G. Wilson v, Jan 09 2002

A067103 a(n) = floor(X/Y), where X = concatenation of cubes and Y = concatenation of natural numbers.

Original entry on oeis.org

1, 1, 14, 148, 14804, 1480398, 148039049, 14803895356, 1480389427723, 148038942652481, 14803894265116205, 1480389426511476635, 148038942651147507639, 14803894265114750596056, 1480389426511475059425814, 148038942651147505942389607, 14803894265114750594238756940
Offset: 1

Views

Author

Robert G. Wilson v, Jan 09 2002

Keywords

Comments

a(n) -> 148038942651147505942387547594667814093751032610233441970375...

Examples

			a(6) = floor(182764125216/123456) = floor(1480398.888802...) = 1480398.

Crossrefs

Cf. A000578, A007908, A019522.
Cf. A067091, A067092, A067093, A067094, A067095, A067096, A067097, A067098, A067099, A067100, A067101, A067102.
See also A066700.

Programs

  • Maple
    a:= n-> floor(parse(cat(i^3$i=1..n))/parse(cat($1..n))):
seq(a(n), n=1..17);  # Alois P. Heinz, May 25 2022
  • Mathematica
    f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[k^3]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 20} ]
nn=20;With[{c=Table[IntegerDigits[n^3],{n,nn}],s=Table[IntegerDigits[n],{n,nn}]}, Table[Floor[FromDigits[Flatten[Take[c,i]]]/FromDigits[Flatten[Take[s,i]]]],{i,nn}]] (* Harvey P. Dale, Feb 10 2013 *)
  • PARI
    c1(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); \\ A007908
c3(n) = my(s=""); for(k=1, n, s=Str(s, k^3)); eval(s); \\ A019522
a(n) = c3(n)\c1(n); \\ Michel Marcus, May 25 2022

A067104 a(n) = floor[ X/Y], where X = concatenation of first n factorials and Y = concatenation of first n natural numbers.

Original entry on oeis.org

1, 1, 1, 10, 1022, 102256, 102255452, 1022553862210, 102255378766606673, 10225537868377981588347, 10225537868286872045185666318, 102255378682858781228966381713174081, 10225537868285867355405173700779791589867289
Offset: 1

Views

Author

Amarnath Murthy, Jan 07 2002

Keywords

Examples

			a(5) = floor [12624120/12345] = floor[1022.60996354799513973268529769137] = 1022.

Links

Crossrefs

Cf. A067091, A067092, A067093, A067094, A067095, A067096, A067097, A067098, A067099, A067100, A067101, A067102, A067103.

Programs

  • Mathematica
    Table[Floor[FromDigits[Flatten[IntegerDigits/@(Range[n]!)]]/FromDigits[ Flatten[IntegerDigits/@Range[n]]]],{n,15}] (* Harvey P. Dale, Jun 09 2020 *)

Extensions

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003
Edited by Charles R Greathouse IV, Apr 27 2010

A277690 Smallest possible number of sides of a regular polygon with unit sides and circumradius at least n.

Original entry on oeis.org

3, 6, 13, 19, 26, 32, 38, 44, 51, 57, 63, 70, 76, 82, 88, 95, 101, 107, 114, 120, 126, 132, 139, 145, 151, 158, 164, 170, 176, 183, 189, 195, 202, 208, 214, 220, 227, 233, 239, 246, 252, 258, 264, 271, 277, 283, 290, 296, 302, 308, 315
Offset: 0

Views

Author

John D. Dixon, Oct 26 2016

Keywords

Comments

The average difference between terms in the sequence approaches 2*Pi.
Limit_{n -> oo} d/dn (Pi / arcsin(1/2n)) = 2*Pi.

Examples

			a(0) = 3, since this is the smallest number of sides a regular polygon may have;
a(1) = ceiling( Pi / arcsin(1/2) ) = ceiling( Pi/(Pi/6) ) = 6;
a(2) = ceiling( Pi / arcsin(1/4) ) = ceiling( Pi/(0.2526...) ) = 13;
...

Crossrefs

See A004082 for another version.
As a function, this is the inverse of A067099.

Programs

  • Mathematica
    Table[If[n == 0, 3, Ceiling[Pi/ArcSin[1/(2 n)]]], {n, 0, 50}] (* Michael De Vlieger, Oct 28 2016 *) (* corrected on Aug 28 2023 by John D. Dixon *)
  • PARI
    a(n) = if (n==0, 3, ceil(Pi/asin(1/(2*n)))); \\ Michel Marcus, Oct 28 2016; corrected Jun 13 2022 \\ corrected again on Aug 28 2023 by John D. Dixon

Formula

a(n) = ceiling( Pi / arcsin(1/(2*n)) ).

Extensions

First term and definition corrected by John D. Dixon, Aug 28 2023

A067105 a(n) = floor[ X/Y], where X = concatenation of k^k from 1 up to n^n and Y = concatenation of 1, ..., n.

Original entry on oeis.org

1, 1, 11, 1156, 1156141, 11560850121, 1156078457100065, 11560777079611640798854, 1156077623683098402586161358986, 1156077622746675519639905953267558458549
Offset: 1

Views

Author

Amarnath Murthy, Jan 07 2002

Keywords

Examples

			a(5) = floor [14272563125/12345] = floor[1156141.20089104900769542324827866] = 1156141.

Crossrefs

Cf. A067091, A067092, A067093, A067094, A067095, A067096, A067097, A067098, A067099, A067100, A067101, A067102, A067103, A067104.

Programs

  • Mathematica
    fxy[n_]:=Module[{num=FromDigits[Flatten[IntegerDigits/@(Table[x^x,{x,n}])]], den=FromDigits[Flatten[IntegerDigits/@Range[n]]]},Floor[num/den]]; Array[ fxy,10] (* Harvey P. Dale, Mar 21 2013 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003
Edited by Charles R Greathouse IV, Apr 28 2010
Showing 1-7 of 7 results.

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