The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A226120

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A226120

Decimal expansion of Sum_{n>=1} n^3/(exp(2*Pi*n/7)-1).
(history; published version)

#19 by Alois P. Heinz at Sat Nov 21 16:59:06 EST 2020

STATUS

editing

approved

#18 by Alois P. Heinz at Sat Nov 21 16:59:04 EST 2020

NAME

Decimal expansion of sum_Sum_{n>=1..infinity} n^3/(exp(2*Pi*n/7)-1).

STATUS

approved

editing

#17 by N. J. A. Sloane at Wed Jan 01 20:42:47 EST 2014

STATUS

proposed

approved

#16 by Rick L. Shepherd at Wed Jan 01 20:12:57 EST 2014

STATUS

editing

proposed

#15 by Rick L. Shepherd at Wed Jan 01 20:12:36 EST 2014

OFFSET

0,2,19

COMMENTS

An almost-integer discovered by Simon Plouffe. The computed sum equals 10 within 17 15 digits.

EXTENSIONS

Offset corrected by Rick L. Shepherd, Jan 01 2014

STATUS

approved

editing

#14 by T. D. Noe at Tue May 28 16:21:35 EDT 2013

STATUS

proposed

approved

#13 by Jean-François Alcover at Tue May 28 14:39:50 EDT 2013

STATUS

editing

proposed

#12 by Jean-François Alcover at Tue May 28 14:36:23 EDT 2013

CROSSREFS

Cf. A060295 (famous almost-integer: Ramanujan's constant), A226121 (another surprising almost-integer by Simon Plouffe), A007775, A089034.

Discussion

Tue May 28

14:39

Jean-François Alcover: Thanks Joerg. I crossref the 2 seqs you quote (and that I didn't know).

#11 by T. D. Noe at Tue May 28 13:17:50 EDT 2013

NAME

Decimal expansion of the surprising almost integer sum_{n=1..infinity} n^3/(exp(2*Pi*n/7)-1) discovered by Simon Plouffe.

COMMENTS

An almost-integer discovered by Simon Plouffe. The computed sum equals 10 within 17 digits.

LINKS

Simon Plouffe, <a href="http://www.plouffe.fr">Simon Plouffe Home Page</a>

Simon Plouffe, <a href="http://www.plouffe.fr">Simon Plouffe Home Page </a>

CROSSREFS

Cf. A060295 (A famous almost -integer: Ramanujan's constant), A226121 (another surprising almost -integer by Simon Plouffe).

STATUS

proposed

editing

#10 by Jean-François Alcover at Tue May 28 09:48:09 EDT 2013

STATUS

editing

proposed

Discussion

Tue May 28

12:20

Joerg Arndt: Try the following Pari code for your amusement:
default(realprecision,110);
{ for (k=1, 100,
    s = sum(n=1, 10^4, n^3/(exp(2*Pi*n/k)-1) );
    print([k, s]);
); }

12:23

Joerg Arndt: Sum is close to integer for k>=7 and not divisible by 2, 3 or 5; cf. A007775.

12:25

Joerg Arndt: Corresponding sums (rounded) are A089034