A305667 Engel expansion whose sum has the concatenation of its terms as decimal part. Case a(1) = 3.

3, 41, 480, 3570, 4893, 7999, 33195, 52784, 72024, 175468, 621177, 832820, 6728999, 8151748, 78184626, 273362479, 883593178, 3960000113, 28999908410, 195575352926, 750833617579, 1453443477101, 9100308145444, 49027044651379, 67795387220152, 78305516479292

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Eric Weisstein's World of Mathematics, Engel expansion

Example

1/3 = 0.3333...
1/3 + 1/(3*41) = 0.341463...
1/3 + 1/(3*41) + 1/(3*41*480) = 0.341480352...
The sum is 0.3 41 480 3570 4893 7999 ...

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, 3);

Crossrefs

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305668.

Sequence in context: A159249 A328509 A087544 * A213378 A189356 A155672

Adjacent sequences: A305664 A305665 A305666 * A305668 A305669 A305670

Keyword

nonn,base

Author

Paolo P. Lava, Jun 12 2018

Extensions

a(5)-a(26) from Giovanni Resta, Jun 12 2018

Status

approved