A304288 Denominators a(n) of the fractions Sum_{n>=1} {n/a(n)} = 1/a(1) + 2/a(2) + 3/a(3) + ... such that the sum has the concatenation of these denominators as decimal part. Case a(1) = 3.

3, 64, 9122, 247449223, 351840295262110531, 628514983855026936648291640964480216

Offset

1,1

Comments

It appears that fractions of this kind exist only for a(1) equal to 3 (this sequence), 10 (A304289), 11 (A305661), 14 (A305662), and 31 (A305663).

a(7) has 73 digits. - Giovanni Resta, Jun 08 2018

Links

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

Example

1/3 = 0.333...
1/3 + 2/64 = 0.364583...
1/3 + 2/64 + 3/9122 = 0.3649122085...
The sum is 0.3 64 9122 ...

Maple

P:=proc(q, h) local a, b, d, n, t; a:=1/h; b:=ilog10(h)+1; d:=h; print(d);
t:=2; for n from 1 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:=t+1; print(n);  fi; od; end: P(10^20, 3);

Crossrefs

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304289, A305661, A305662, A305663, A305664, A305665, A305666.

Sequence in context: A231823 A174841 A084883 * A275044 A205645 A326429

Adjacent sequences: A304285 A304286 A304287 * A304289 A304290 A304291

Keyword

nonn,base

Author

Paolo P. Lava, Jun 08 2018

Extensions

a(4)-a(6) from Giovanni Resta, Jun 08 2018

Status

approved