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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
OFFSET
1,1
COMMENTS
At any step only the least value greater than a(n) is taken into consideration.
LINKS
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);
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, May 17 2019
EXTENSIONS
a(4)-a(6) from Giovanni Resta, May 17 2019
STATUS
approved