A305661 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) = 11.

11, 75, 795297, 93992106533, 45114643856137363285734, 5244406139948692731854965782168773850666243474

Offset

1,1

Comments

It appears that fractions of this kind exist only for a(1) equal to 3 (A304288), 10 (A304289), 11 (this sequence), 14 (A305662), and 31 (A304663).

a(7) has 92 digits. - Giovanni Resta, Jun 08 2018

Links

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

Example

1/11 = 0.090909... At the beginning instead of 11 we have 09 as first decimal digits. Adding the second term this is fixed.
1/11 + 2/75 = 0.117575...
1/11 + 2/75 + 3/795297 = 0.1175795297514...
The sum is 0.11 75 795297 93992106533 ...

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, 11);

Crossrefs

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305662, A305663, A305664, A305665, A305666.

Sequence in context: A300925 A347987 A157232 * A287330 A282384 A092225

Adjacent sequences: A305658 A305659 A305660 * A305662 A305663 A305664

Keyword

nonn,base

Author

Paolo P. Lava, Jun 08 2018

Extensions

a(3)-a(6) from Giovanni Resta, Jun 08 2018

Status

approved