A137991 Decimal expansion of the inverse of the number whose Engel expansion has the sequence of Fibonacci numbers (A000045) as coefficients.

3, 6, 9, 7, 5, 3, 7, 1, 7, 1, 4, 8, 0, 8, 9, 0, 9, 6, 5, 4, 5, 2, 9, 4, 7, 8, 8, 9, 3, 2, 9, 1, 2, 0, 8, 6, 2, 0, 4, 7, 6, 0, 7, 3, 5, 8, 0, 7, 6, 3, 4, 9, 4, 9, 9, 5, 7, 3, 5, 9, 7, 2, 8, 4, 6, 8, 6, 5, 2, 8, 4, 0, 3, 4, 5, 3, 1, 9, 2, 8, 6, 0, 7, 7, 2, 3, 9, 7, 5, 1, 0, 0, 3, 0, 0, 7, 2, 6, 8

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Feb 26 2008

Keywords

• easy
• nonn
• cons

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Eric Weisstein's World of Mathematics, Pierce Expansion.
• Eric Weisstein's World of Mathematics, Engel Expansion.

Crossrefs

Cf. A000045, A101689 (reciprocal), A137987.

Programs

Maple

with (combinat,fibonacci); P:=proc(n) local a,i,k; a:=0; k:=1; for i from 1 by 1 to n do k:=k*fibonacci(i); a:=a+1/k; print(evalf(1/a,100)); od; end: P(100);

Mathematica

RealDigits[N[1/(Sum[Product[1/Fibonacci[k], {k, 1, n}], {n, 1, 1000}]),
100]][[1]] (* G. C. Greubel, Dec 26 2016 *)