

A320284


Pierce expansion whose sum has the concatenation of its terms as decimal part. Case a(1) = 3.


10




OFFSET

1,1


COMMENTS

a(10) is the last term because the sequence cannot be further extended (see A305668 for the reason why in a similar sequence).  Giovanni Resta, Oct 11 2018


LINKS



EXAMPLE

1/3 = 0.3333...
1/3  1/(3*322) = 0.33229813...
1/3  1/(3*322) + 1/(3*322*991) = 0.33229918124...
1/3  1/(3*322) + 1/(3*322*991)  1/(3*322*991*8111)= 0.332299181115244...
The sum is 0.3 322 991 8111 ...


MAPLE

P:=proc(q, h) local a, b, c, d, n, t, x; x:=1;
a:=1/h; b:=ilog10(h)+1; c:=h; d:=h; print(d); t:=1;
for n from x to q do if trunc(evalf(a+(1)^t/(c*n), 500)*10^(b+ilog10(n)+1))=d*10^(ilog10(n)+1)+n
then x:=n+1; b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+(1)^t/(c*n); c:=c*n; t:=t+1; print(n); fi; od; end: P(10^9, 3);


CROSSREFS



KEYWORD

nonn,base,fini,full


AUTHOR



EXTENSIONS



STATUS

approved



