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Revision History for A294826

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A294826

Numerators of the partial sums of the reciprocals of twice the heptagonal numbers (k + 1)*(5*k + 2) = A135706(k+1) = 2*A000566(k+1), for k >= 0.
(history; published version)

#24 by Harvey P. Dale at Thu Aug 31 17:29:49 EDT 2023

STATUS

editing

approved

#23 by Harvey P. Dale at Thu Aug 31 17:29:45 EDT 2023

MATHEMATICA

Accumulate[1/(2*PolygonalNumber[7, Range[30]])]//Numerator (* Harvey P. Dale, Aug 31 2023 *)

STATUS

approved

editing

#22 by Charles R Greathouse IV at Thu Sep 08 08:46:20 EDT 2022

PROG

(MAGMAMagma) [Numerator((&+[1/((k+1)*(5*k+2)): k in [0..n]])): n in [0..25]]; // G. C. Greubel, Aug 29 2018

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#21 by Michael De Vlieger at Tue Mar 22 15:34:22 EDT 2022

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proposed

approved

#20 by Michel Marcus at Tue Mar 22 11:31:30 EDT 2022

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editing

proposed

#19 by Michel Marcus at Tue Mar 22 11:31:14 EDT 2022

COMMENTS

The limit of the series is V(5,2) = lim_{n -> oo} V(5,2;n) = ((5/2)*log(5) - (2*phphi-1)*(log(phi) - (Pi/5)*sqrt(7-4*phi)))/6, with the golden section phi:= (1 + sqrt(5))/2. The value is 0.661389626561... given by (1/2)*A244639.

STATUS

approved

editing

Discussion

Tue Mar 22

11:31

Michel Marcus: typo: phi rather than ph

#18 by Bruno Berselli at Thu Aug 30 03:03:16 EDT 2018

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reviewed

approved

#17 by Michel Marcus at Thu Aug 30 00:46:51 EDT 2018

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proposed

reviewed

#16 by G. C. Greubel at Wed Aug 29 23:22:43 EDT 2018

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editing

proposed

#15 by G. C. Greubel at Wed Aug 29 23:22:37 EDT 2018

LINKS

G. C. Greubel, <a href="/A294826/b294826.txt">Table of n, a(n) for n = 0..600</a>

STATUS

proposed

editing