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 A307021 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(1)+a(2)) + 1/(a(1)+a(2)+a(3)) + ... begins with the concatenation of these numbers; also a(1) = 10 and a(n) > a(n-1). 6
 10, 95, 45660, 4880278340, 53661584146863422613, 3948698587495271884779444899313333936634 (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. As a(2) we could choose 95, 311, ... Next term has 81 digits. - Giovanni Resta, Mar 20 2019 LINKS Table of n, a(n) for n=1..6. Eric Weisstein's World of Mathematics, Egyptian fraction EXAMPLE 1/10 = 0.1000... 1/10 + 1/(10+95) = 0.1095238... 1/10 + 1/(10+95) + 1/(10+95+45660) = 0.109545660283... The sum is 0.10 95 45660 ... 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 1 to q do z:=evalf(evalf(a+1/(t+n), 100)*10^(b+ilog10(n)+1), 100); z:=trunc(z-frac(z)); if z=d*10^(ilog10(n)+1)+n then b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; t:=t+n; a:=a+1/(t); print(n); fi; od; end: P(10^20, 10) CROSSREFS Cf. A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305667, A305668, A307007, A307020, A307022, A320023, A320284, A320306, A320307, A320308, A320309, A320335, A320336, A324222, A324223. Sequence in context: A190987 A233738 A277441 * A197083 A197086 A278359 Adjacent sequences: A307018 A307019 A307020 * A307022 A307023 A307024 KEYWORD nonn,more AUTHOR Paolo P. Lava, Mar 20 2019 EXTENSIONS a(4)-a(6) from Giovanni Resta, Mar 20 2019 STATUS approved

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Last modified April 19 11:31 EDT 2024. Contains 371792 sequences. (Running on oeis4.)