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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 (list; graph; refs; listen; history; text; internal format)
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)
CROSSREFS
Sequence in context: A190987 A233738 A277441 * A197083 A197086 A278359
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Mar 20 2019
EXTENSIONS
a(4)-a(6) from Giovanni Resta, Mar 20 2019
STATUS
approved

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Last modified April 19 11:31 EDT 2024. Contains 371792 sequences. (Running on oeis4.)