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.

A105731 Odd numbers k such that A105658(k) != k.

Original entry on oeis.org

13, 17, 23, 25, 37, 41, 43, 47, 49, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 75, 77, 81, 83, 85, 97, 99, 103, 107, 111, 117, 121, 123, 125, 127, 129, 131, 137, 139, 143, 145, 149, 151, 153, 157, 159, 161, 163, 169, 173, 177, 179, 181, 183, 189, 191, 193, 195, 197
Offset: 1

Views

Author

Jess E. Boling (tdbpeekitup(AT)yahoo.com) and Robert G. Wilson v, Apr 18 2005

Keywords

Crossrefs

Cf. A105658, A105732, A105733, A105769.

Programs

  • Mathematica
    f[n_] := f[n] = Product[i^i, {i, n}]/Denominator[ Sum[j(j + 1)/2/(Product[j!/k!, {k, 0, j - 1}]), {j, n}]]; Select[ Range[1, 200, 2], f[ # ] != # &]

A105732 Even numbers k such that A105658(k) != k/2.

Original entry on oeis.org

16, 24, 26, 32, 40, 42, 44, 50, 54, 56, 58, 64, 84, 86, 96, 100, 102, 104, 106, 108, 110, 124, 128, 132, 136, 140, 144, 146, 148, 152, 156, 162, 164, 168, 170, 172, 174, 180, 182, 184, 186, 188, 192, 198, 204, 206, 212, 214, 224, 226, 228, 234, 236, 240, 242
Offset: 1

Views

Author

Jess E. Boling (tdbpeekitup(AT)yahoo.com) and Robert G. Wilson v, Apr 18 2005

Keywords

Crossrefs

Cf. A105658, A105731, A105733, A105769.

Programs

  • Mathematica
    f[n_] := f[n] = Product[i^i, {i, n}]/Denominator[Sum[j(j + 1)/2/(Product[j!/k!, {k, 0, j - 1}]), {j, n}]]; Select[ Range[2, 242, 2], 2f[ # ] != # &]

A105769 a(n) = A105658(n)/k, where k=n if n is odd, else k=n/2.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 13, 55, 1, 1, 1, 1, 1, 175, 325, 13, 253, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 5, 1, 1, 19, 11, 19, 5, 35, 1, 1, 629, 1, 253, 29, 1, 1, 29, 31, 43, 37, 5, 13, 43, 1, 1219, 1, 55, 5, 186599, 1, 72283, 1, 29, 1, 47, 1, 1, 1, 1711, 1, 25, 1, 1, 1, 67, 1
Offset: 1

Views

Author

Jess E. Boling (tdbpeekitup(AT)yahoo.com) and Robert G. Wilson v, Apr 18 2005

Keywords

Comments

Records: 1,11,13,55,175,325,629,1219,186599,6298799,24804047515,..., which occur at: 1,13,16,17,23,24,47,61,65,180,337,...

Crossrefs

Cf. A105658, A105731, A105732.

Programs

  • Mathematica
    f[n_] := f[n] = Product[i^i, {i, n}]/Denominator[Sum[j(j + 1)/2/(Product[j!/k!, {k, 0, j - 1}]), {j, n}]]; Table[ If[ OddQ[n], f[n]/n, 2f[n]/n], {n, 82}]

A105733 Numbers k such that A105658(2k-1) != 2k-1 and A105658(2k) != k.

Original entry on oeis.org

12, 13, 21, 22, 25, 27, 28, 29, 32, 42, 43, 50, 52, 54, 62, 64, 66, 70, 72, 73, 76, 81, 82, 85, 87, 90, 91, 92, 96, 99, 102, 103, 106, 112, 117, 120, 122, 123, 126, 129, 131, 132, 135, 140, 142, 144, 147, 152, 154, 155, 158, 159, 162, 169
Offset: 1

Views

Author

Jess E. Boling (tdbpeekitup(AT)yahoo.com) and Robert G. Wilson v, Apr 18 2005

Keywords

Crossrefs

Cf. A105658, A105731, A105732, A105769.

Programs

  • Mathematica
    f[n_] := f[n] = Product[i^i, {i, n}]/Denominator[Sum[j(j + 1)/2/(Product[j!/k!, {k, 0, j - 1}]), {j, n}]]; Select[ Range[125], f[2# - 1] != 2# - 1 && f[2# ] != # &]

A107952 Increasing partial quotients in A107951.

Original entry on oeis.org

1, 4, 6, 23, 25, 36, 84, 499, 857, 1393, 1741, 1961, 106527, 130617, 257090, 1912295, 2647129
Offset: 1

Views

Author

Robert G. Wilson v, May 28 2005

Keywords

Comments

Positions of the increasingly larger partial quotients are in A106643.

Crossrefs

Cf. A107951, A107950, A105658.

Programs

  • Mathematica
    cf = ContinuedFraction[ Sum[i(i + 1)/2/Product[i!/j!, {j, 0, i - 1}], {i, 1500}]]; a = 0; Do[ If[ cf[[n]] > a, a = cf[[n]]; Print[a]], {n, 6462686}]

A107950 Boling's constant, the decimal expansion of Sum_{i>=1} i(i+1) / (2*Product_{j=0..i-1} i!/j!).

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, May 28 2005

Keywords

Examples

			B=1.805917418986691013997505385851050680989652545909634282575958858...

Crossrefs

Cf. A105658, A107951, A107952.

Programs

  • Mathematica
    RealDigits[ Sum[i(i + 1)/2/Product[i!/j!, {j, 0, i - 1}], {i, 14}], 10, 111][[1]]
Clear[B]; B[m_] := B[m] = N[Sum[i*(1+i)/2*BarnesG[1+i]/i!^i, {i, 1, m}], 105]; m=2; While[B[m] != B[m-1], m++]; RealDigits[B[m]][[1]] (* Jean-François Alcover, Nov 18 2015 *)

A107951 Continued fraction expansion of Boling's constant.

Original entry on oeis.org

1, 1, 4, 6, 1, 1, 3, 1, 2, 5, 23, 3, 1, 1, 2, 1, 2, 1, 6, 2, 1, 5, 1, 12, 8, 2, 1, 1, 1, 4, 6, 1, 12, 6, 1, 1, 3, 1, 2, 2, 3, 1, 1, 1, 1, 25, 3, 2, 1, 1, 1, 3, 2, 1, 4, 3, 7, 36, 1, 3, 19, 1, 3, 11, 2, 7, 2, 4, 1, 6, 5, 20, 3, 1, 1, 4, 1, 84, 10, 4, 2, 1, 3, 3, 1, 1, 2, 1, 2, 1, 1, 1, 499, 2, 12, 1, 4, 857
Offset: 0

Views

Author

Robert G. Wilson v, May 28 2005

Keywords

Crossrefs

Cf. A107950 (decimal expansion), A105658, A107952.

Programs

  • Mathematica
    ContinuedFraction[ Sum[i(i + 1)/2/Product[i!/j!, {j, 0, i - 1}], {i, 20}]]

Extensions

Offset changed by Andrew Howroyd, Aug 03 2024
Showing 1-7 of 7 results.

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