Revision History for A020793
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#55 by Michael De Vlieger at Tue Aug 06 09:57:18 EDT 2024
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#54 by Michel Marcus at Tue Aug 06 02:25:09 EDT 2024
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#53 by Andrew Howroyd at Mon Aug 05 23:17:49 EDT 2024
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Discussion
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| Mon Aug 05
| 23:28
| Andrew Howroyd: Rather add to https://www.thefactsite.com/number-6-facts/
Or https://facts.net/number-6-facts/
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| Tue Aug 06
| 00:32
| Elmo R. Oliveira: @Andrew, with all due respect to your approach, but I don't understand the deletion of my comments. Below, I present notes regarding the comments:
> Comment #1: I say this because there is in A136375 cites 5/66 as the 10th Bernoulli number. In A177057 there is Comment: 7/6 is the 14th Bernoulli number. Given the acceptance of the OEIS, I would like your evaluation in order to maintain this comment.
> Comment #2: As for the continued fraction (sqrt(10) - 2) proposed, I checked it on PARI and it results in = [1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], that is, it corresponds to this sequence. Therefore, I request your analysis in order to maintain this comment as well.
Thanks again.
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#52 by Andrew Howroyd at Mon Aug 05 23:17:39 EDT 2024
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| FORMULA
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From _E.g.f.: 6*exp(x) - 5. - _Elmo R. Oliveira_, Aug 05 2024: (Start)
E.g.f.: 6*exp(x) - 5.
a(n) = 6 - 5*0^n = 6, n >= 1. (End)
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#51 by Andrew Howroyd at Mon Aug 05 23:12:24 EDT 2024
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| COMMENTS
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From Elmo R. Oliveira, Aug 05 2024: (Start)
1/6 is the 2nd Bernoulli number.
Continued fraction expansion of sqrt(10) - 2. (End)
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| FORMULA
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a(n) = 6 - 5*0^n = 6, n >= 1.. (End)
a(n) = 6 - A020761(n). (End)
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| CROSSREFS
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Cf. A000367/A002445 (Bernoulli numbers B_2n), A020761.
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proposed
editing
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#50 by Elmo R. Oliveira at Mon Aug 05 20:37:57 EDT 2024
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#49 by Elmo R. Oliveira at Mon Aug 05 20:36:20 EDT 2024
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| COMMENTS
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From Elmo R. Oliveira, Aug 05 2024: (Start)
1/6 is the 2nd Bernoulli number.
Continued fraction expansion of sqrt(10) - 2. (End)
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| REFERENCES
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Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Springer, 2013. See, see p. 224.
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| FORMULA
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From Elmo R. Oliveira, Aug 05 2024: (Start)
E.g.f.: 6*exp(x) - 5.
a(n) = 6 - 5*0^n = 6, n >= 1.
a(n) = 6 - A020761(n). (End)
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| CROSSREFS
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Cf. A010722, A021019, A021028, A021100, A021388, A040006, A070064, A071279, A081822, A101272, A168608, A177057, A272001, A272002.
Cf. A000367/A002445 (Bernoulli numbers B_2n), A020761.
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| STATUS
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approved
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#48 by N. J. A. Sloane at Mon Jul 01 13:16:48 EDT 2024
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#47 by Stefano Spezia at Mon Jul 01 12:57:18 EDT 2024
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#46 by Stefano Spezia at Mon Jul 01 12:57:13 EDT 2024
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| FORMULA
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K_{n>=2} 2*n/(2*n - 3) = 5/3. (Seesee Clawson at p. 224). - Stefano Spezia, Jul 01 2024
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| STATUS
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proposed
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