

A305668


Engel expansion whose sum has the concatenation of its terms as decimal part. Case a(1) = 10.


12




OFFSET

1,1


COMMENTS

a(7) is the last term because the sequence cannot be extended. At any step a(n) is chosen as the least number greater than a(n1) that meets the requirement. Up to 8110039 the sum is 0.10 100 316 5169 183766 972915 8110039 008537... but the next term would be less than 1/(10*100*316*5169*183766*972915*8110039^2) = 0.00 000 000 0000 000000 000000 00000000 005206195... and the zeros after 8110039 cannot be removed.


LINKS

Table of n, a(n) for n=1..7.
Eric Weisstein's World of Mathematics, Engel expansion


EXAMPLE

1/10 = 0.10000...
1/10 + 1/(10*100) = 0.10100000...
1/10 + 1/(10*100) + 1/(10*100*316) = 0.10100316455...
The sum is 0.10 100 316 5169 ...


MAPLE

P:=proc(q, h) local a, b, c, d, n, x; x:=1; a:=1/h; b:=ilog10(h)+1;
c:=h; d:=h; print(d); for n from x to q do if trunc(evalf(a+1/(c*n), 100)*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/(c*n); c:=c*n; print(n); fi; od; end: P(10^9, 10);


CROSSREFS

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305667.
Sequence in context: A207770 A207897 A207657 * A262761 A134556 A207449
Adjacent sequences: A305665 A305666 A305667 * A305669 A305670 A305671


KEYWORD

nonn,base,fini,full


AUTHOR

Paolo P. Lava, Jun 12 2018


EXTENSIONS

a(5)a(7) from Giovanni Resta, Jun 12 2018


STATUS

approved



