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%I #7 Oct 11 2018 14:11:03
%S 3,322,991,8111,52473,60206,529366,957640,7693680,69425274
%N Pierce expansion whose sum has the concatenation of its terms as decimal part. Case a(1) = 3.
%C 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
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>.
%e 1/3 = 0.3333...
%e 1/3 - 1/(3*322) = 0.33229813...
%e 1/3 - 1/(3*322) + 1/(3*322*991) = 0.33229918124...
%e 1/3 - 1/(3*322) + 1/(3*322*991) - 1/(3*322*991*8111)= 0.332299181115244...
%e The sum is 0.3 322 991 8111 ...
%p P:=proc(q, h) local a, b, c, d, n, t, x; x:=1;
%p a:=1/h; b:=ilog10(h)+1; c:=h; d:=h; print(d); t:=1;
%p 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
%p 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);
%Y Cf. A305667, A305668.
%K nonn,base,fini,full
%O 1,1
%A _Paolo P. Lava_, Oct 09 2018
%E a(5)-a(10) from _Giovanni Resta_, Oct 11 2018
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