A325726 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(2)-a(1)) + 1/(a(3)-a(2)+a(1)) + ... begins with the concatenation of these numbers; also a(1) = 10 and a(n) > a(n-1).

10, 321, 688679, 648399312079, 795011217364419041371938, 378887020322265448186183258957408252353018723756

Offset

1,1

Comments

At any step only the least value greater than a(n) is taken into consideration. In fact, instead of 321, as a(2) we could choose 515, 1290, ...

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/(321-10) = 0.10321543...
1/10 + 1/(321-10) + 1/(688679-321+10) = 0.10321688679494...
The sum is 0.10 321 688679 ...

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 t+1 to q do
z:=evalf(evalf(a+1/(n-t), 100)*10^(b+length(n)), 100);
z:=trunc(z-frac(z)); if z=d*10^length(n)+n then b:=b+length(n);
d:=d*10^length(n)+n; t:=n-t; 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, A307021, A307022, A320023, A320284, A320306, A320307, A320308, A320309, A320335, A320336, A324222, A324223, A325725, A325727, A325728.

Sequence in context: A302933 A180584 A048345 * A223298 A164055 A064343

Adjacent sequences: A325723 A325724 A325725 * A325727 A325728 A325729

Keyword

nonn,base

Author

Paolo P. Lava, May 17 2019

Extensions

a(4)-a(6) from Giovanni Resta, May 17 2019

Status

approved