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 A077469 #12 May 22 2025 19:37:59
%S A077469 1,5,16,21,29,35,39,52,57,63,68,76,82,88,93,99,106,113,118,127,134,
%T A077469 150,155,160,167,172,182,192,197,209,215,224,229,237,242,246,260,265,
%U A077469 272,278,289,293,310,315,320,330,337,346,353,373,379,384,390,396,405,416
%N A077469 Greedy powers of (3/4): Sum_{n>=1} (3/4)^a(n) = 1.
%C A077469 The n-th greedy power of x, when 0.5 < x < 1, is the smallest integer exponent a(n) that does not cause the power series Sum_{k=1..n} x^a(k) to exceed unity.
%C A077469 A heuristic argument suggests that the limit of a(n)/n is m - Sum_{n>=m} log(1 + x^n)/log(x) = 8.0547475948..., where x=3/4 and m=floor(log(1-x)/log(x))=4. - _Paul D. Hanna_, Nov 16 2002
%F A077469 a(n) = Sum_{k=1..n} floor(g(k)) where g(1)=1, g(n+1)=log_x(x^frac(g_n) - x) at x=(3/4) and frac(y) = y - floor(y).
%F A077469 a(n) seems to be asymptotic to c*n with c around 8.0... - _Benoit Cloitre_
%e A077469 a(3)=9 since (3/4) +(3/4)^5 +(3/4)^16 < 1 and (3/4) +(3/4)^5 +(3/4)^15 > 1.
%t A077469 s = 0; a = {}; Do[ If[s + (3/4)^n < 1, s = s + (3/4)^n; a = Append[a, n]], {n, 1, 428}]; a
%t A077469 heuristiclimit[x_] := (m=Floor[Log[x, 1-x]])+1/24+Log[x, Product[1+x^n, {n, 1, m-1}]/DedekindEta[I Log[x]/-Pi]*DedekindEta[ -I Log[x]/2/Pi]]; N[heuristiclimit[3/4], 20]
%Y A077469 Cf. A077468, A077470, A077471, A077472, A077473, A077474, A077475.
%K A077469 easy,nonn
%O A077469 1,2
%A A077469 _Paul D. Hanna_, Nov 06 2002
%E A077469 Edited and extended by _Robert G. Wilson v_, Nov 08 2002. Also extended by _Benoit Cloitre_, Nov 06 2002