

A320335


Numerators of the fractions a(0)/(a(1)  a(0)), a(1)/(a(2)  a(1)), a(2)/(a(3)  a(2)), ... such that the sum Sum_{n>=1} a(n1)/(a(n)  a(n1)) has the concatenation of these numerators, starting from a(1), as decimal part. Case a(0) = 1, a(1) = 4.


11




OFFSET

0,2


COMMENTS

It appears that fractions of this kind with a(0)=1 exist only for a(1) equal to 4 (this sequence) and 13 (A320336).


LINKS



EXAMPLE

1/(41) = 0.3333...
At the beginning instead of 4 we have 3 as first decimal digit. Adding the second term this is fixed.
1/(41) + 4/(41  4) = 0.441441...
1/(41) + 4/(41  4) + 41/(89814  41) = 0.44189814891 ...
The sum is 0.4 41 89814 98285430640360 ...


MAPLE

P:=proc(q, h) local a, b, d, t, x, n; x:=1; a:=1/(h1); b:=ilog10(h1)+1; d:=h; print(d); t:=h; for n from h+1 to q do if trunc(evalf(a+t/(nt), 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/(nt); t:=n; x:=n+1; print(n); fi; od; end: P(10^10, 4);


CROSSREFS

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A320306, A320307, A320308, A320309, A320336.


KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



