|
%I #16 Jun 19 2021 09:43:37
%S 1,4,23,937574,9717339108198104,
%T 997945570689257470816576227568765689032610
%N Denominators of the fraction Sum_{n>=0} {a(n)/a(n+1)} = a(0)/a(1) + a(1)/a(2) + a(2)/a(3) + ... such that the sum has the concatenation of these denominators as decimal part. Case a(0) = 1 and a(1) = 4.
%C It appears that there are only three sequences of this kind, with a(1) = 3 (A305664), a(1) = 4 (this sequence) and a(1) = 10 (A305666).
%C a(6) has 110 digits. - _Giovanni Resta_, Jun 08 2018
%e 1/4 = 0.3333...
%e 1/4 + 4/23 = 0.3407043...
%e 1/4 + 4/23 + 23/937574= 0.34076600381136...
%e The sum is 0.3 407 6600381 ...
%p P:=proc(q,h) local a,b,d,n,t,x; x:=1; a:=1/h; b:=ilog10(h)+1;
%p d:=h; print(d); t:=1/a; for n from x to q do
%p 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:=n; x:=n+1; print(n); fi; od; end: P(10^20,4);
%Y Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305664, A305666.
%K nonn,base
%O 0,2
%A _Paolo P. Lava_, Jun 08 2018
%E a(4)-a(5) from _Giovanni Resta_, Jun 08 2018
%E a(0)=1 inserted. - _R. J. Mathar_, Jun 19 2021
| 