A305663 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) = 31.

31, 7, 975425, 85939741154, 936552965614980263201, 933486208332286775628057914016814688052592

Offset

1,1

Comments

It appears that fractions of this kind exist only for a(1) equal to 3 (A304288), 10 (A304289), 11 (A305661), 14 (A305662), and 31 (this sequence).

For each of the other cases, the terms of the sequence are in increasing order, but this sequence begins with 31, 7, ... (see Example).

a(7) has 84 digits. - Giovanni Resta, Jun 08 2018

Links

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

Example

1/31 = 0.03225... At the beginning instead of 31 we have 03 as first decimal digits. Adding the second term this is fixed.
1/31 + 2/7 = 0.317972...
1/31 + 2/7 + 3/975425 = 0.317975425812...
The sum is 0.31 7 975425...

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, 31);

Crossrefs

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305664, A305665, A305666.

Sequence in context: A187810 A347592 A174129 * A040936 A029821 A040935

Adjacent sequences: A305660 A305661 A305662 * A305664 A305665 A305666

Keyword

nonn,base

Author

Paolo P. Lava, Jun 08 2018

Extensions

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

Status

approved