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A307021
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) = 10 and a(n) > a(n-1).
6
10, 95, 45660, 4880278340, 53661584146863422613, 3948698587495271884779444899313333936634
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 95, 311, ...
Next term has 81 digits. - Giovanni Resta, Mar 20 2019
LINKS
Eric Weisstein's World of Mathematics, Egyptian fraction
EXAMPLE
1/10 = 0.1000...
1/10 + 1/(10+95) = 0.1095238...
1/10 + 1/(10+95) + 1/(10+95+45660) = 0.109545660283...
The sum is 0.10 95 45660 ...
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, 10)
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Mar 20 2019
EXTENSIONS
a(4)-a(6) from Giovanni Resta, Mar 20 2019
STATUS
approved