A159354 - OEIS

%I #18 Sep 08 2022 08:45:43

%S 1,3,6,4,4,6,7,6,6,6,5,6,1,3,1,2,5,7,3,9,8,6,4,2,9,0,8,5,0,0,3,7,6,2,

%T 3,6,6,1,8,7,9,9,6,7,7,5,3,5,3,8,7,3,9,0,1,1,0,3,6,7,9,7,7,2,1,5,8,5,

%U 5,3,0,7,2,7,2,7,3

%N Decimal expansion of 18 - 24*log(2).

%C The sum of the reciprocals of the nonnegative square pyramidal numbers (A000330).

%H G. C. Greubel, <a href="/A159354/b159354.txt">Table of n, a(n) for n = 1..10000</a>

%H E. Pérez Herrero, <a href="http://psychedelic-geometry.blogspot.com/2009/04/square-pyramidal-numbers-reciprocals.html">Square Pyramidal Numbers Reciprocals Sum</a>, Psychedelic Geometry Blogspot

%H pipi, <a href="http://math.stackexchange.com/questions/317336/how-to-evaluate-sum-limits-n-1-infty-frac11k2k-cdotsnk?rq=1">How to evaluate sum_{n>=1} 1/(1^k+2^k+...+n^k) ?</a>, math.stackexchange, Feb 28 2013

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Sum_{k>=1} 1/(n*(n+1)*(2*n+1)/6). - _Joerg Arndt_, Dec 08 2013

%t Sum[1/Sum[i^2, {i, 1, k}], {k, 1, Infinity}]

%t RealDigits[18-24*Log[2],10,100][[1]] (* _G. C. Greubel_, Jun 15 2018 *)

%o (PARI) 18 - 24*log(2) \\ _G. C. Greubel_, Jun 15 2018

%o (Magma) 18 - 24*Log(2); // _G. C. Greubel_, Jun 15 2018

%Y Cf. A000292.

%K cons,nonn

%O 1,2

%A _Enrique Pérez Herrero_, Apr 11 2009