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A325725
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) = 3 and a(n) > a(n-1).
2
3, 53, 5254, 942711270, 60527555104759884, 6079815437830353357655363418656533, 36605822957679968262595918562001251109330115418597396926274122249725
OFFSET
1,1
COMMENTS
At any step only the least value greater than a(n) is taken into consideration. In fact, instead of 53, as a(2) we could choose 76, 367, 3366, 3666, 33367, 34350, 333366, ...
LINKS
Eric Weisstein's World of Mathematics, Egyptian fraction
EXAMPLE
1/3 = 0.3333...
1/3 + 1/(53-3) = 0.353333...
1/3 + 1/(53-3) + 1/(5254-53+3) = 0.3535254932...
The sum is 0.3 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, 3);
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, May 17 2019
EXTENSIONS
a(4) - a(7) from Giovanni Resta, May 17 2019
STATUS
approved