OFFSET
1,1
COMMENTS
a(6) is the last term because the sequence cannot be extended. At any step a(n) is chosen as the least number greater than a(n-1) that meets the requirement. Up to 960 the sum is 0.3 32 37 64 533 960 0692... and the zero after 960 cannot be removed.
If the limitation a(n) > a(n-1) were removed then the sequence would be 3, 32, 37, 22, 48 and 48 would be the last term because after it the sum presents 0911... and the zero cannot be removed. - Giovanni Resta, Feb 20 2019
EXAMPLE
1/3^1 = 0.3333...
1/3^1 - 1/32^2 = 0.332356...
1/3^1 - 1/32^2 + 1/37^3 = 0.33237651...
The sum is 0.3 32 37 64 533 ...
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+(-1)^(t+1)/n^t, 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+(-1)^(t-1)/n^t; t:=t+1;
print(n); fi; od; end: P(10^6, 3);
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Paolo P. Lava, Feb 18 2019
EXTENSIONS
a(6) added by Giovanni Resta, Feb 20 2019
STATUS
approved