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 A077474 #14 May 22 2025 21:55:54
%S A077474 1,4,8,18,21,28,31,36,41,44,55,58,71,76,79,84,88,108,125,135,141,148,
%T A077474 155,158,164,175,180,185,195,198,218,225,230,237,242,246,250,254,259,
%U A077474 263,268,276,281,300,305,310,317,321,326,329,334,340,343,351,359,364
%N A077474 Greedy powers of (7/10): Sum_{n>=1} (7/10)^a(n) = 1.
%C A077474 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 A077474 A heuristic argument suggests that the limit of a(n)/n is m - Sum_{n>=m} log(1 + x^n)/log(x) = 5.9293123466..., where x=7/10 and m=floor(log(1-x)/log(x))=3. - _Paul D. Hanna_, Nov 16 2002
%F A077474 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=7/10 and frac(y) = y - floor(y).
%F A077474 a(n) seems to be asymptotic to c*n with c around 6... - _Benoit Cloitre_
%e A077474 a(3)=8 since (7/10) +(7/10)^3 +(7/10)^8 < 1 and (7/10) +(7/10)^3 +(7/10)^7 > 1.
%t A077474 s = 0; a = {}; Do[ If[s + (7/10)^n < 1, s = s + (7/10)^n; a = Append[a, n]], {n, 1, 368}]; a
%t A077474 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[7/10], 20]
%Y A077474 Cf. A077468, A077469, A077470, A077471, A077472, A077473, A077475.
%K A077474 easy,nonn
%O A077474 1,2
%A A077474 _Paul D. Hanna_, Nov 06 2002
%E A077474 Edited and extended by _Robert G. Wilson v_, Nov 08 2002; also extended by _Benoit Cloitre_, Nov 06 2002