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)
CROSSREFS
KEYWORD
base,nonn,more
AUTHOR
Paolo P. Lava, Mar 20 2019
EXTENSIONS
a(4)-a(7) from Giovanni Resta, Mar 20 2019
STATUS
approved