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 A325725 a(n) is defined by the condition that the decimal expansion of the Sum_{n>=1} 1/(Sum_{k=1..n} a(k)) = 1/a(1) + 1/(a(2)-a(1)) + 1/(a(3)-a(2)+a(1)) + ... begins with the concatenation of these numbers; also a(1) = 3 and a(n) > a(n-1). 2
 3, 53, 5254, 942711270, 60527555104759884, 6079815437830353357655363418656533, 36605822957679968262595918562001251109330115418597396926274122249725 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS At any step only the least value greater than a(n) is taken into consideration. In fact, instead of 53, as a(2) we could choose 76, 367, 3366, 3666, 33367, 34350, 333366, ... LINKS Eric Weisstein's World of Mathematics, Egyptian fraction EXAMPLE 1/3 = 0.3333... 1/3 + 1/(53-3) = 0.353333... 1/3 + 1/(53-3) + 1/(5254-53+3) = 0.3535254932... The sum is 0.3 53 5254 ... MAPLE P:=proc(q, h) local a, b, d, n, t, z; a:=1/h; b:=length(h); d:=h; print(d); t:=h; for n from t+1 to q do z:=evalf(evalf(a+1/(n-t), 100)*10^(b+length(n)), 100); z:=trunc(z-frac(z)); if z=d*10^length(n)+n then b:=b+length(n); d:=d*10^length(n)+n; t:=n-t; a:=a+1/t; print(n); fi; od; end: P(10^20, 3); CROSSREFS Cf. A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305667, A305668, A307007, A307020, A307021, A307022, A320023, A320284, A320306, A320307, A320308, A320309, A320335, A320336, A324222, A324223, A325726, A325727, A325728. Sequence in context: A301348 A296680 A118194 * A173357 A144537 A208631 Adjacent sequences:  A325722 A325723 A325724 * A325726 A325727 A325728 KEYWORD nonn,base AUTHOR Paolo P. Lava, May 17 2019 EXTENSIONS a(4) - a(7) from Giovanni Resta, May 17 2019 STATUS approved

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Last modified September 19 17:51 EDT 2021. Contains 347564 sequences. (Running on oeis4.)