This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A110020 #13 Feb 16 2025 08:32:58 %S A110020 1,2,5,12,8,2,5,7,3,2,5,4,6,13,7,2,11,15,6,2,36,13,2,6,3,7,3,4,2,9,4, %T A110020 2,2,2,2,2,6,5,2,3,2,2,2,2,11,3,59,8,2,4,104,103,5,6,2,2,2,59,2,2,3,9, %U A110020 20,4,2,3,4,3,4,2,2,2,2,2,2,4,3,4,2,3,2,37,2,49,6,2,6,10,2,4,8,15,2,2,23,2 %N A110020 Final term of the simple continued fraction for H(n), where H(n) = Sum_{k=1..n} 1/k. %H A110020 G. C. Greubel, <a href="/A110020/b110020.txt">Table of n, a(n) for n = 1..1000</a> %H A110020 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a> %H A110020 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a> %e A110020 H(5) = 137/60 = 2 + 1/(3 + 1/(1 + 1/(1 + 1/8))); a(5) is the final term, 8. %t A110020 Table[Last[ContinuedFraction[HarmonicNumber[n]]], {n, 100}] (* _Ray Chandler_, Sep 17 2005 *) %Y A110020 m-th harmonic number H(m) = A001008(m)/A002805(m). %Y A110020 Cf. A055573, A058027, A100398, A112286, A112287. %K A110020 easy,nonn %O A110020 1,2 %A A110020 _Leroy Quet_, Sep 03 2005 %E A110020 Extended by _Ray Chandler_, Sep 17 2005