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A307022
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(1)+a(2)) + 1/(a(1)+a(2)+a(3)) + ... begins with the concatenation of these numbers; also a(1) = 3 and a(n) > a(n-1).
6
3, 51, 9558, 98612460, 5887957252067828, 499453888097584722752603691410216, 64374739267553439324757181002125046128361976093811234838816138018
OFFSET
1,1
COMMENTS
At any step only the least value greater than a(n) is taken into consideration. As a(2) we could choose 51, 360, 3363, 33363, ..., 3...363.
Next term has 131 digits. - Giovanni Resta, Mar 20 2019
LINKS
Eric Weisstein's World of Mathematics, Egyptian fraction
EXAMPLE
1/3 = 0.3333...
1/3 + 1/(3+51) = 0.351851...
1/3 + 1/(3+51) + 1/(3+51+9558) = 0.3519558884...
The sum is 0.3 51 9558 ...
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 1 to q do
z:=evalf(evalf(a+1/(t+n), 100)*10^(b+ilog10(n)+1), 100);
z:=trunc(z-frac(z)); if z=d*10^(ilog10(n)+1)+n then b:=b+ilog10(n)+1;
d:=d*10^(ilog10(n)+1)+n; t:=t+n; a:=a+1/(t); print(n);
fi; od; end: P(10^20, 3)
KEYWORD
base,nonn,more
AUTHOR
Paolo P. Lava, Mar 20 2019
EXTENSIONS
a(4)-a(7) from Giovanni Resta, Mar 20 2019
STATUS
approved