A305664 Denominators of the fraction Sum_{n>=0} {a(n)/a(n+1)} = a(0)/a(1) + a(1)/a(2) + a(2)/a(3) + ... such that the sum has the concatenation of these denominators as decimal part. Case a(0) = 1 and a(1) = 3.

1, 3, 407, 6600381, 17430443514717989342, 6151641599894174777009497253213101162115020503132036

Offset

0,2

Comments

It appears that there are only three sequences of this kind, with a(1) = 3 (this sequence), a(1) = 4 (A305665) and a(1) = 10 (A305666).

a(6) has 136 digits. - Giovanni Resta, Jun 08 2018

Links

Table of n, a(n) for n=0..5.

Example

1/3 = 0.3333...
1/3 + 3/407 = 0.3407043...
1/3 + 3/407 + 407/6600381= 0.34076600381136...
The sum is 0.3 407 6600381 ...

Maple

P:=proc(q, h) local a, b, d, n, t, x; x:=1; a:=1/h; b:=ilog10(h)+1;
d:=h; print(d); t:=1/a; for n from x to q do
if trunc(evalf(a+t/n, 100)*10^(b+ilog10(n)+1))=d*10^(ilog10(n)+1)+n then b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+t/n; t:=n; x:=n+1; print(n); fi; od; end: P(10^20, 3);

Crossrefs

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305665, A305666.

Sequence in context: A181990 A198666 A330014 * A152517 A333134 A366355

Adjacent sequences: A305661 A305662 A305663 * A305665 A305666 A305667

Keyword

nonn,base

Author

Paolo P. Lava, Jun 08 2018

Extensions

a(4)-a(5) from Giovanni Resta, Jun 08 2018

a(0)=1 inserted. - R. J. Mathar, Jun 19 2021

Status

approved