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A304289 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) = 10. 26

%I #11 Jun 09 2018 15:45:10

%S 10,447,801562,802579930803,6452460179149463130736799,

%T 63264179795423791266127232983907572653187775508481

%N 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) = 10.

%C It appears that fractions of this kind exist only for a(1) equal to 3 (A304288), 10 (this sequence), 11 (A305661), 14 (A305662), and 31 (A305663).

%C a(7) has 101 digits. - _Giovanni Resta_, Jun 08 2018

%e 1/10 = 0.10000...

%e 1/10 + 2/447 = 0.10447427...

%e 1/10 + 2/447 + 3/801562 = 0.10447801562304...

%e The sum is 0.1 447 801562 ...

%p P:=proc(q,h) local a,b,d,n,t; a:=1/h; b:=ilog10(h)+1; d:=h; print(d);

%p 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(10^20,10);

%Y Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A305661, A305662, A305663, A305664, A305665, A305666.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Jun 08 2018

%E a(4)-a(6) from _Giovanni Resta_, Jun 08 2018

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)