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 1-3 of 3 results.

A048799 Decimal expansion of Sum_{n >= 2} 1/S(n)!, where S(n) is the Kempner number A002034(n).

Original entry on oeis.org

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

Views

Author

Charles T. Le (charlestle(AT)yahoo.com)

Keywords

Comments

Computed using suggestions from David W. Wilson posted to Sequence Fans mailing list (seqfan(AT)ext.jussieu.fr), May 30 2002
By the time n = 100 in the Mathematica coding below, each term < 10^-143.
I conjecture that the constants defined in the present sequence, A048834, A071120, A048835, A048836, A048837, A048838 are irrational. - Sukanto Bhattacharya (susant5au(AT)yahoo.com.au), Apr 28 2008

Examples

			1.09317...

References

  • I. Cojocaru, S. Cojocaru, First Constant of Smarandache, Smarandache Notions Journal, Vol. 7, No. 1-2-3, 1996, 116-118.

Links

Crossrefs

Cf. A071120, A002034, A048834, A038024, A048834, A071120, A048835, A048836, A048837, A048838.

Programs

  • Mathematica
    f[n_] := DivisorSigma[0, n! ]; s = 1; Do[s = N[s + (f[n + 1] - f[n])/(n + 1)!, 100], {n, 1, 10^4}]; RealDigits[s][[1]]

Formula

Sum (1/S(n)!), where S(n) is the Kempner function A002034 and n >= 2.
Sum (A038024(n)/n!), where A038024(n) = #{k: S(k) = n} and n >= 2. - Jonathan Sondow, Aug 21 2006

Extensions

Edited by Robert G. Wilson v and Don Reble, May 30 2002

A083872 Triangle read by rows in which row n lists first appearance of m such that m divides n!.

Original entry on oeis.org

1, 2, 3, 6, 4, 8, 12, 24, 5, 10, 15, 20, 30, 40, 60, 120, 9, 16, 18, 36, 45, 48, 72, 80, 90, 144, 180, 240, 360, 720, 7, 14, 21, 28, 35, 42, 56, 63, 70, 84, 105, 112, 126, 140, 168, 210, 252, 280, 315, 336, 420, 504, 560, 630, 840, 1008, 1260, 1680, 2520, 5040, 32, 64
Offset: 1

Views

Author

Jon Perry, Jun 18 2003

Keywords

Comments

Differs from A110797 starting at a(17)=9.
From Rémy Sigrist, Sep 17 2017: (Start)
Each number k > 0 appears exactly once in the triangle, on row A002034(k).
The n-th row of the triangle:
- contains A038024(n) terms,
- starts with A046021(n),
- ends with n! = A000142(n).
(End)

Examples

			1!:1
2!:1,2 -> 2 as 1 has already appeared
3!:1,2,3,6 -> 3,6
4!:1,2,3,4,6,8,12,24 -> 4,8,12,24

Links

Crossrefs

Cf. A000142, A002034, A038024, A046021.

Programs

Extensions

Extended by Ray Chandler, Aug 23 2005

A071120 Decimal expansion of Sum_{n >= 1} 1/S(n)!, where S(n) is the Kempner number A002034.

Original entry on oeis.org

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

Views

Author

Charles T. Le (charlestle(AT)yahoo.com)

Keywords

Comments

Computed using suggestions from David W. Wilson posted to Sequence Fans mailing list (seqfan(AT)ext.jussieu.fr), May 30 2002

Examples

			2.09317...

References

  • I. Cojocaru, S. Cojocaru, First Constant of Smarandache, Smarandache Notions Journal, Vol. 7, No. 1-2-3, 1996, 116-118.

Links

Crossrefs

Cf. A048799, A002034, A048834, A038024, A092495.

Programs

  • Mathematica
    f[n_] := DivisorSigma[0, n! ]; s = 1; Do[s = N[s + (f[n + 1] - f[n])/(n + 1)!, 100], {n, 1, 10^4}]; RealDigits[s][[1]]

Formula

Sum_{n>=1} 1/S(n)!, where S(n) is the Kempner function A002034.
Sum_{n>=1} A038024(n)/n!, where A038024(n) = #{k: S(k) = n}. - Jonathan Sondow, Aug 21 2006
Equals 1+A048799.

Extensions

Edited by Robert G. Wilson v and Don Reble, May 30 2002
Showing 1-3 of 3 results.

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