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

0,3

Links

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Harmonic Mean.

Eric Weisstein's World of Mathematics, Lerch Transcendent.

Wikipedia, Harmonic mean.

Formula

a(n) = denominator(1/(1/2^n - Re(Phi(2, 1, n+1)))), where Phi(z, s, a) is the Lerch transcendent.

Example

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, ...

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

Crossrefs

Cf. A353250 (numerators).

Cf. A003149, A136128, A241519, A242376.

Sequence in context: A281998 A294676 A293465 * A271924 A354427 A178712

Adjacent sequences: A353248 A353249 A353250 * A353252 A353253 A353254

Keyword

nonn,frac

Author

Vladimir Reshetnikov, Apr 08 2022

Status

approved