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 A351738 #27 Aug 12 2022 19:02:32
%S A351738 1,7,1,5,6,7,1,7,9,4,7,0,9
%N A351738 Decimal expansion of Sum_{k>0} sin(sqrt(k)) / k.
%C A351738 Sum_{k>0} sin(k^alpha) / (k^beta) with 0 < alpha < 1 is convergent if beta > max(alpha, 1-alpha); the constant of this sequence corresponds to the case alpha = 1/2 and beta = 1 (see Arnaudiès).
%C A351738 Consequence: Sum_{k>0} sin(k^(1/m)) / k converges for any positive integer m.
%C A351738 The sequence converges slowly.
%D A351738 J. M. Arnaudiès, P. Delezoide et H. Fraysse, Exercices résolus d'Analyse du cours de mathématiques - 2, Dunod, 1993, Exercice 11, pp. 316-319.
%H A351738 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/828323/convergence-of-sum-k-1-infty-sin-left-sqrtk-right-k">Convergence of Sum_{k=0..infinity} sin(sqrt(k)) / k</a>.
%e A351738 1.715671794709...
%o A351738 (PARI) default(realprecision, 100); sumalt(k=0, sum(j=1+floor(k^2*Pi^2),floor((k+1)^2*Pi^2), sin(sqrt(j))/j)) \\ _Vaclav Kotesovec_, May 21 2022
%Y A351738 Cf. A096418, A096444, A114940, A228639, A263193, A342680.
%K A351738 nonn,cons,more
%O A351738 1,2
%A A351738 _Bernard Schott_, May 20 2022
%E A351738 More digits from _Stefano Spezia_, May 21 2022