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%I #24 Oct 09 2017 17:57:35
%S 6,2,6,6,3,6,1,3,8,7,8,9,4,3,6,3,3,9,7,1,9,2,2,4,1,1,7,2,8,0,9,6,2,6,
%T 5,9,2,4,4,0,8,3,3,3,8,4,3,4,3,3,6,9,0,0,2,6,3,1,3,2,9,0,6,2,4,9,2,3,
%U 0,1,1,1,6,8,1,4,8,8,7,4,8,3,9,5,1,4,3,9,6,9,5,4,5,8,9,7,7,2,3,8,0,9,0,9,9,7,7,7,3,6,8,4,8,2,9,5,1,0,8,4,7,1,7,2,5,0,4,4,9,4,3,7,7,4,3,5,3,4,8,8,3,9,5,5,5,7,3,6,7,4
%N Decimal expansion of: Sum_{n>=1} -1 / (n * (1/2 - 2^n)^n).
%C This constant plus A292179 equals log(2), due to the identity (at x = 1/2):
%C Sum_{n=-oo..+oo, n<>0} (x - x^n)^n / n = -log(1-x).
%H Paul D. Hanna, <a href="/A292178/b292178.txt">Table of n, a(n) for n = 0..500</a>
%F Constant: Sum_{n>=1} -(-1)^n * 2^n / (n * (2^(n+1) - 1)^n).
%F Constant: log(2) - Sum_{n>=1} (2^(n-1) - 1)^n / (n * 2^(n^2)).
%e Constant t = 0.62663613878943633971922411728096265924408333843433690026313290...
%e where t = 2/(1*3) - 4/(2*7^2) + 8/(3*15^3) - 16/(4*31^4) + 32/(5*63^5) - 64/(6*127^6) + 128/(7*255^7) - 256/(8*511^8) + 512/(9*1023^9) - 1024/(10*2047^10) + 2048/(11*4095^11) - 4096/(12*8191^12) + 8192/(13*16383^13) - 16384/(14*32767^14) + 32768/(15*65535^15) +...
%e Also,
%e log(2) - t = 0/(1*2) + 1^2/(2*2^4) + 3^3/(3*2^9) + 7^4/(4*2^16) + 15^5/(5*2^25) + 31^6/(6*2^36) + 63^7/(7*2^49) + 127^8/(8*2^64) + 255^9/(9*2^81) + 511^10/(10*2^100) + 1023^11/(11*2^121) + 2047^12/(12*2^144) + 4095^13/(13*2^169) + 8191^14/(14*2^196) + 16383^15/(15*2^225) +... (constant A292179)
%Y Cf. A292179.
%K nonn,cons
%O 0,1
%A _Paul D. Hanna_, Oct 05 2017
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