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

1/11 + 1/(52-11) + 1/(9943537-52+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/(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);

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

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