A325728 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) = 14 and a(n) > a(n-1).

14, 28, 71192, 3951239529, 91599717337708557840, 25287155431709811559363106042646332272281

Offset

1,1

Comments

At any step only the least value greater than a(n) is taken into consideration.

Links

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

Eric Weisstein's World of Mathematics, Egyptian fraction

Example

1/14 = 0.071428...
1/14 + 1/(28-14) = 0.1428571...
1/14 + 1/(28-14) + 1/(71192-28+14) = 0.142871192142...
The sum is 0.14 28 71192...

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, 14);

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, A325726, A325727.

Sequence in context: A067295 A212890 A019552 * A305662 A174070 A045527

Adjacent sequences: A325725 A325726 A325727 * A325729 A325730 A325731

Keyword

nonn,base

Author

Paolo P. Lava, May 17 2019

Extensions

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

Status

approved