A325725 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) = 3 and a(n) > a(n-1).

3, 53, 5254, 942711270, 60527555104759884, 6079815437830353357655363418656533, 36605822957679968262595918562001251109330115418597396926274122249725

Offset

1,1

Comments

At any step only the least value greater than a(n) is taken into consideration. In fact, instead of 53, as a(2) we could choose 76, 367, 3366, 3666, 33367, 34350, 333366, ...

Links

Table of n, a(n) for n=1..7.

Eric Weisstein's World of Mathematics, Egyptian fraction

Example

1/3 = 0.3333...
1/3 + 1/(53-3) = 0.353333...
1/3 + 1/(53-3) + 1/(5254-53+3) = 0.3535254932...
The sum is 0.3 53 5254 ...

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, 3);

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, A325726, A325727, A325728.

Sequence in context: A301348 A296680 A118194 * A173357 A144537 A208631

Adjacent sequences: A325722 A325723 A325724 * A325726 A325727 A325728

Keyword

nonn,base

Author

Paolo P. Lava, May 17 2019

Extensions

a(4) - a(7) from Giovanni Resta, May 17 2019

Status

approved