

A307022


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) = 3 and a(n) > a(n1).


6




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 51, 360, 3363, 33363, ..., 3...363.
Next term has 131 digits.  Giovanni Resta, Mar 20 2019


LINKS

Table of n, a(n) for n=1..7.
Eric Weisstein's World of Mathematics, Egyptian fraction


EXAMPLE

1/3 = 0.3333...
1/3 + 1/(3+51) = 0.351851...
1/3 + 1/(3+51) + 1/(3+51+9558) = 0.3519558884...
The sum is 0.3 51 9558 ...


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(zfrac(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, 3)


CROSSREFS

Cf. A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305667, A305668, A307007, A307020, A307021, A320023, A320284, A320306, A320307, A320308, A320309, A320335, A320336, A324222, A324223.
Sequence in context: A275798 A246050 A091502 * A330302 A227067 A261187
Adjacent sequences: A307019 A307020 A307021 * A307023 A307024 A307025


KEYWORD

nonn,more


AUTHOR

Paolo P. Lava, Mar 20 2019


EXTENSIONS

a(4)a(7) from Giovanni Resta, Mar 20 2019


STATUS

approved



