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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(n-1). 3
11, 52, 9943537, 9881972526746, 9201489001757012121335125, 82921502495183923916318126922414429034029157972857 (list; graph; refs; listen; history; text; internal format)



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


Table of n, a(n) for n=1..6.

Eric Weisstein's World of Mathematics, Egyptian fraction


1/11 = 0.090909...

1/11 + 1/(52-11) = 0.1152993...

1/11 + 1/(52-11) + 1/(9943537-52+11) = 0.11529943537979...

The sum is 0.11 53 5254 ...


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, 11);


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




Paolo P. Lava, May 17 2019


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



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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)