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).

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

Table of n, a(n) for n=1..6.

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

Cf. A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305667, A305668, A307007, A307020, A307022, A320023, A320284, A320306, A320307, A320308, A320309, A320335, A320336, A324222, A324223.

Sequence in context: A190987 A233738 A277441 * A197083 A197086 A278359

Adjacent sequences: A307018 A307019 A307020 * A307022 A307023 A307024

Keyword

nonn,more

Author

Paolo P. Lava, Mar 20 2019

Extensions

a(4)-a(6) from Giovanni Resta, Mar 20 2019

Status

approved