A320284 Pierce expansion whose sum has the concatenation of its terms as decimal part. Case a(1) = 3.

3, 322, 991, 8111, 52473, 60206, 529366, 957640, 7693680, 69425274

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

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Pierce Expansion.

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

Cf. A305667, A305668.

Sequence in context: A080976 A228192 A272318 * A235334 A160070 A112895

Adjacent sequences: A320281 A320282 A320283 * A320285 A320286 A320287

Keyword

nonn,base,fini,full

Author

Paolo P. Lava, Oct 09 2018

Extensions

a(5)-a(10) from Giovanni Resta, Oct 11 2018

Status

approved