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 1-8 of 8 results.

A067121 a(n) = floor[X/Y] where X = the concatenation of the first n even numbers in increasing order and Y = their sum.

Original entry on oeis.org

1, 4, 20, 123, 8227, 587643, 44073235, 3427918353, 274233468240, 22437283765107, 1869773647092288, 158211616292424373, 13560995682207803419, 1175286292458009629726, 102837550590075842601095
Offset: 1

Views

Author

Amarnath Murthy, Jan 08 2002

Keywords

Examples

			a(4): floor[2468/(2+4+6+8)] = floor[123.4] = 123.

Links

Crossrefs

Cf. A067112-A067120.

Programs

  • Maple
    for i from 1 to 33 do n := 2*i:s := n:c := n:n := n-2:while(n>0) do s := s+n:g := floor(log(c+1)/log(10)):c := c+10^(g+1)*n:n := n-2:end do:a[i] := floor(c/s):end do:q := seq(a[j],j=1..33);
  • Mathematica
    Module[{nn=20,ev},ev=2*Range[nn];Table[Floor[FromDigits[Flatten[ IntegerDigits/@ Take[ev,n]]]/(n^2+n)],{n,nn}]] (* Harvey P. Dale, Dec 05 2014 *)

Extensions

More terms from Sascha Kurz, Mar 23 2002

A067119 a(n) = floor[X/Y] where X = concatenation of first n even numbers in increasing order and Y = n-th triangular number.

Original entry on oeis.org

2, 8, 41, 246, 16454, 1175286, 88146471, 6855836706, 548466936480, 44874567530214, 3739547294184576, 316423232584848746, 27121991364415606839, 2350572584916019259453, 205675101180151685202190
Offset: 1

Views

Author

Amarnath Murthy, Jan 08 2002

Keywords

Examples

			a(4) = floor[2468/(1+2+3+4)] = floor[246.8] = 246.

Links

Crossrefs

Cf. A067112-A067118.

Programs

  • Maple
    for i from 1 to 33 do n := 2*i:c := n:n := n-2:while(n>0) do g := floor(log(c+1)/log(10)):c := c+10^(g+1)*n:n := n-2:end do:a[i] := floor(2*c/i/(i+1)):end do:q := seq(a[j],j=1..33);
  • Mathematica
    Module[{nn=20},Table[Floor[FromDigits[Flatten[IntegerDigits/@Range[2,2n,2]]]/((n(n+1))/2)],{n,nn}]] (* Harvey P. Dale, Oct 03 2019 *)

Extensions

More terms from Sascha Kurz, Mar 23 2002
Edited by Charles R Greathouse IV, Apr 27 2010

A067120 a(n) = floor(X/Y) where X = concatenation of first n odd numbers in increasing order and Y = n-th triangular number.

Original entry on oeis.org

1, 4, 22, 135, 905, 64662, 4849682, 377197536, 30175802922, 2468929330031, 205744110835938, 17409117070733232, 1492210034634277058, 129324869668304011738, 11315926095976601027106, 998464067292053031803477, 88752361537071380604753549, 7941000769106386685688475516
Offset: 1

Views

Author

Amarnath Murthy, Jan 08 2002

Keywords

Examples

			a(4) floor[1357/(1+2+3+4)] = floor[135.7] = 135.

Links

Crossrefs

Cf. A067112-A067119.

Programs

  • Maple
    for i from 1 to 33 do n := 2*i-1:c := n:n := n-2:while(n>0) do g := floor(log(c)/log(10)):c := c+10^(g+1)*n:n := n-2:end do:a[i] := floor(2*c/i/(i+1)):end do:q2 := seq(a[j],j=1..33);
  • Mathematica
    With[{nn=20},Table[Floor[FromDigits[Flatten[IntegerDigits/@Range[1,2n-1,2]]]/((n(n+1))/2)],{n,nn}]] (* Harvey P. Dale, Feb 22 2020 *)

Extensions

More terms from Sascha Kurz, Mar 23 2002
Edited by Charles R Greathouse IV, Apr 27 2010

A067122 Floor[X/Y] where X = concatenation of first n odd numbers in increasing order (A019519) and Y = their sum (A000290 = n^2).

Original entry on oeis.org

1, 3, 15, 84, 543, 37719, 2771247, 212173614, 16764334957, 1357911131517, 112224060455966, 9429938413313834, 803497710956918416, 69281180179448577716, 6035160584520853881123, 530434035748903173145597
Offset: 1

Views

Author

Amarnath Murthy, Jan 08 2002

Keywords

Examples

			a(4) = floor[1357/16] = floor[84.8125] =84.

Crossrefs

Cf. A067112-A067121, A072723.

Extensions

More terms from Henry Bottomley, Jul 07 2002

A067114 Let N = 24681012141618202224262830..., the concatenation of the even numbers. Then a(n) = sum of first n digits of N.

Original entry on oeis.org

2, 6, 12, 20, 21, 21, 22, 24, 25, 29, 30, 36, 37, 45, 47, 47, 49, 51, 53, 57, 59, 65, 67, 75, 78, 78, 81, 83, 86, 90, 93, 99, 102, 110, 114, 114, 118, 120, 124, 128, 132, 138, 142, 150, 155, 155, 160, 162, 167, 171, 176, 182, 187, 195, 201, 201, 207, 209, 215, 219
Offset: 1

Views

Author

Amarnath Murthy, Jan 08 2002

Keywords

Examples

			a(5) = 2+4+6+8+1 = 21.

Crossrefs

Cf. A067112, A067113.

Programs

  • Mathematica
    Accumulate[Flatten[IntegerDigits/@Range[2,66,2]]] (* Harvey P. Dale, Nov 09 2011 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

A067115 Let N = 1357911131517192123252729... = concatenation of odd numbers. Then a(n) = sum of first n digits of N.

Original entry on oeis.org

1, 4, 9, 16, 25, 26, 27, 28, 31, 32, 37, 38, 45, 46, 55, 57, 58, 60, 63, 65, 70, 72, 79, 81, 90, 93, 94, 97, 100, 103, 108
Offset: 1

Views

Author

Amarnath Murthy, Jan 08 2002

Keywords

Examples

			a(6)= 1+3+5+7+9+1 = 26.

Links

Crossrefs

Cf. A067112, A067113, A067114.

Programs

  • Mathematica
    Module[{nn=20,codd},codd=Flatten[IntegerDigits/@(2Range[0,nn]+1)];Accumulate[ codd]] (* Harvey P. Dale, Jul 09 2021 *)

A067118 a(n) =floor[X/Y] where X= concatenation of first n even numbers in decreasing order and Y = that of first n odd numbers in increasing order.

Original entry on oeis.org

2, 3, 4, 6, 8, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 76, 78, 79, 81, 82, 84, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103
Offset: 1

Views

Author

Amarnath Murthy, Jan 08 2002

Keywords

Examples

			a(4) = floor[8642/1357] = floor[6.368...] = 6.

Crossrefs

Cf. A067112-A067117.

Programs

  • Maple
    for i from 1 to 50 do c := 2:n := 4:m := 2*i-1:d := m:m := m-2:while(m>0) do g := floor(log(c+1)/log(10)):c := c+10^(g)*n:n := n+2:g := floor(log(d)/log(10)): d := d+10^(g+1)*m:m := m-2:end do:a[i] := floor(c/d):end do:q := seq(a[j],j=1..50);
  • Mathematica
    Table[Floor[FromDigits[Flatten[IntegerDigits/@Range[2n,2,-2]]]/FromDigits[ Flatten[IntegerDigits/@Range[1,2n-1,2]]]],{n,80}] (* Harvey P. Dale, Nov 02 2013 *)

Extensions

More terms from Sascha Kurz, Mar 23 2002
Edited by Charles R Greathouse IV, Apr 27 2010

A067123 Floor[X/Y] where X = concatenation of first n cubes in increasing order and Y = concatenation of first n squares.

Original entry on oeis.org

1, 1, 12, 12, 122, 1225, 12252, 122526, 1225268, 12252682, 122526828, 1225268284, 12252682845, 122526828457, 1225268284577, 12252682845779, 122526828457797, 1225268284577978, 12252682845779785, 122526828457797852
Offset: 1

Views

Author

Amarnath Murthy, Jan 08 2002

Keywords

Examples

			a(5) = floor[182764125/1491625] = floor[122.526858292131065113550657839604] = 122.

Links

Crossrefs

Cf. A067112-A067122.

Programs

  • Mathematica
    fxy[n_]:=Module[{c=FromDigits[Flatten[IntegerDigits/@(Range[n]^3)]],s = FromDigits[ Flatten[ IntegerDigits/@(Range[n]^2)]]}, Floor[c/s]]; Array[fxy,20] (* Harvey P. Dale, Aug 06 2020 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003
Showing 1-8 of 8 results.

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