A071527 Numbers k such that the simple continued fraction for (1+1/k)^k contains k.

2, 3, 7, 8, 15, 17, 18, 24, 32, 45, 54, 59, 90, 100, 112, 114, 128, 135, 144, 249, 270, 419, 452, 517, 557, 674, 701, 822, 916, 1074, 1274, 1643, 2137, 2180, 2272, 2519, 2539, 3049, 3294, 3666, 3907, 4405, 4463, 4478, 4848, 5226, 5446, 7058, 7189, 7857, 8966, 9430

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..95

Example

(1+1/17)^17 has for continued fraction [2, 1, 1, 1, 3, 1, 10, 1, 2, 1, 4, 5, 4, 3, 2, 1, 2, 37, 3, 5, 3, 2, 1, 14, 1, 17, 1, 22, 1, 2, 1, 1, 1, 1, 2, 2, 16, 2, 2, 1, 1, 1, 10, 2, 5, 2] which contains 17 hence 17 is in the sequence.

Mathematica

For[n=1, n<=3000, n++, {r=(1+1/n)^n; If[MemberQ[ContinuedFraction[r], n], Print[n]]}]
Select[Range[6000], MemberQ[ContinuedFraction[(1+1/#)^#], #]&] (* Harvey P. Dale, May 03 2011 *)

Prog

(PARI) for(n=1, 150, if(prod(i=1, length(contfrac((1+1/n)^n)), n-component(contfrac((1+1/n)^n), i))==0, print1(n, ", ")))

Crossrefs

Sequence in context: A033082 A084406 A075648 * A307328 A097095 A101755

Adjacent sequences: A071524 A071525 A071526 * A071528 A071529 A071530

Keyword

nonn

Author

Benoit Cloitre, Jun 02 2002

Extensions

More terms from John W. Layman, Apr 26 2004

More terms from Harvey P. Dale, May 03 2011.

More terms from Amiram Eldar, Sep 05 2020

Status

approved