A353251 a(0) = 1, a(n) = harmonic_mean(a(n-1), n), where harmonic_mean(p, q) = 2/(1/p + 1/q); denominators.
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
Examples
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, ...
Links
- Eric Weisstein's World of Mathematics, Harmonic Mean.
- Eric Weisstein's World of Mathematics, Lerch Transcendent.
- Wikipedia, Harmonic mean.
Programs
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Mathematica
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
Formula
a(n) = denominator(1/(1/2^n - Re(Phi(2, 1, n+1)))), where Phi(z, s, a) is the Lerch transcendent.