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%I #6 Jun 12 2018 21:13:09
%S 3,41,480,3570,4893,7999,33195,52784,72024,175468,621177,832820,
%T 6728999,8151748,78184626,273362479,883593178,3960000113,28999908410,
%U 195575352926,750833617579,1453443477101,9100308145444,49027044651379,67795387220152,78305516479292
%N Engel expansion whose sum has the concatenation of its terms as decimal part. Case a(1) = 3.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EngelExpansion.html ">Engel expansion</a>
%e 1/3 = 0.3333...
%e 1/3 + 1/(3*41) = 0.341463...
%e 1/3 + 1/(3*41) + 1/(3*41*480) = 0.341480352...
%e The sum is 0.3 41 480 3570 4893 7999 ...
%p 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);
%p 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
%p then x:=n+1; b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+1/(c*n); c:=c*n;
%p print(n); fi; od; end: P(10^9,3);
%Y Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305668.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Jun 12 2018
%E a(5)-a(26) from _Giovanni Resta_, Jun 12 2018