A241519
Denominators of b(n) = b(n-1)/2 + 1/(2*n), b(0)=0.
Original entry on oeis.org
1, 2, 2, 12, 3, 15, 60, 840, 105, 630, 630, 13860, 6930, 180180, 360360, 144144, 9009, 306306, 306306, 11639628, 14549535, 14549535, 58198140, 2677114440, 334639305, 3346393050
Offset: 0
0, 1/2, 1/2, 5/12, 1/3, 4/15, 13/60, 151/840, 16/105, 83/630, 73/630, ...
b(1) = (0+1)/2, hence a(1)=2.
b(2) = (1/2+1/2)/2 = 1/2, hence a(2)=2.
b(3) = (1/2+1/3)/2 = 5/12, hence a(3)=12.
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b[0] = 0; b[n_] := b[n] = 1/2*(b[n-1] + 1/n); Table[b[n] // Denominator, {n, 0, 25}] (* Jean-François Alcover, Apr 25 2014 *)
Table[-Re[LerchPhi[2, 1, n + 1]], {n, 0, 20}] // Denominator (* Eric W. Weisstein, Dec 11 2017 *)
-Re[LerchPhi[2, 1, Range[20]]] // Denominator (* Eric W. Weisstein, Dec 11 2017 *)
RecurrenceTable[{b[n] == b[n - 1]/2 + 1/(2 n), b[0] == 0}, b[n], {n, 20}] // Denominator (* Eric W. Weisstein, Dec 11 2017 *)
A353250
a(0) = 1, a(n) = harmonic_mean(a(n-1), n), where harmonic_mean(p, q) = 2/(1/p + 1/q); numerators.
Original entry on oeis.org
1, 1, 4, 24, 48, 480, 960, 13440, 26880, 161280, 322560, 7096320, 14192640, 369008640, 738017280, 295206912, 590413824, 20074070016, 40148140032, 1525629321216, 15256293212160, 30512586424320, 61025172848640, 2807157951037440, 5614315902074880
Offset: 0
a(0) = 1,
a(1) = 2/(1/1 + 1/1) = 1,
a(2) = 2/(1/1 + 1/2) = 4/3,
a(3) = 2/(1/(4/3) + 1/3) = 24/13,
a(4) = 2/(1/(24/13) + 1/4) = 48/19, etc.
This sequence gives the numerators: 1, 1, 4, 24, 48, ...
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Table[1/(1/2^n - Re[LerchPhi[2, 1, n + 1]]), {n, 0, 24}] // Numerator (* or *)
a[0] = 1; a[n_Integer] := a[n] = 2/(1/a[n-1] + 1/n); Table[a[n], {n, 0, 24}] // Numerator
A353251
a(0) = 1, a(n) = harmonic_mean(a(n-1), n), where harmonic_mean(p, q) = 2/(1/p + 1/q); denominators.
Original entry on oeis.org
1, 1, 3, 13, 19, 143, 223, 2521, 4201, 21563, 37691, 737161, 1328521, 31463413, 57821173, 21404465, 39854897, 1267947073, 2383173185, 85428430547, 808549483039, 1535039635999, 2921975382559, 128230606647497, 245195521274057, 2348840786785261, 4508193056814061
Offset: 0
a(0) = 1,
a(1) = 2/(1/1 + 1/1) = 1,
a(2) = 2/(1/1 + 1/2) = 4/3,
a(3) = 2/(1/(4/3) + 1/3) = 24/13,
a(4) = 2/(1/(24/13) + 1/4) = 48/19, etc.
This sequence gives the denominators: 1, 1, 3, 13, 19, ...
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Table[1/(1/2^n - Re[LerchPhi[2, 1, n + 1]]), {n, 0, 26}] // Denominator (* or *)
a[0] = 1; a[n_Integer] := a[n] = 2/(1/a[n-1] + 1/n); Table[a[n], {n, 0, 26}] // Denominator
Showing 1-3 of 3 results.
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