

A325727


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) = 11 and a(n) > a(n1).


3




OFFSET

1,1


COMMENTS

At any step only the least value greater than a(n) is taken into consideration.


LINKS

Table of n, a(n) for n=1..6.
Eric Weisstein's World of Mathematics, Egyptian fraction


EXAMPLE

1/11 = 0.090909...
1/11 + 1/(5211) = 0.1152993...
1/11 + 1/(5211) + 1/(994353752+11) = 0.11529943537979...
The sum is 0.11 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/(nt), 100)*10^(b+length(n)), 100);
z:=trunc(zfrac(z)); if z=d*10^length(n)+n then b:=b+length(n);
d:=d*10^length(n)+n; t:=nt; a:=a+1/t; print(n); fi; od; end:
P(10^20, 11);


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, A325726, A325728.
Sequence in context: A304280 A231386 A191099 * A004622 A045471 A086715
Adjacent sequences: A325724 A325725 A325726 * A325728 A325729 A325730


KEYWORD

nonn,base


AUTHOR

Paolo P. Lava, May 17 2019


EXTENSIONS

a(4)a(6) from Giovanni Resta, May 17 2019


STATUS

approved



