A181691 Numbers k such that Fibonacci(k) has exactly two 1's.

19, 26, 27, 37, 40, 47, 51, 56, 61, 64, 68, 69, 70, 72, 79, 84, 86, 87, 92, 97, 98, 99, 102, 108, 113, 121, 135, 138, 140, 144, 153, 154, 162, 164, 167, 178, 183, 185, 191, 228, 235, 250, 251, 252, 257, 269, 292, 306

Offset

1,1

Comments

No more terms < 10000. Is the sequence finite?

No more terms < 100000. - Harvey P. Dale, Apr 02 2012

From David A. Corneth, Sep 04 2025: (Start)

Probably finite and full given the number of ones tends to increase (cf. A085855) and the terms must be too large given the expected number of ones way over 2.

No more terms < 10^7.

Generally for n > 306 it is enough to check the last 150 digits of Fibonacci(k) to find more than two 1's. For k = 355 we have Fibonacci(k) has only one digit 1.

To check all candidates < 10^7 it was needed to check the last 204 digits to find more than 2 ones if there were more than 2 ones as Fibonacci(1650886) has the third one from the right at 10^203. (End)

Links

Table of n, a(n) for n=1..48.

Example

From David A. Corneth, Sep 04 2025: (Start)
56 is in the sequence as Fibonacci(56) = 225851433717 which has exactly two ones.
307 is not in the sequence as Fibonacci(307) ends in 109298792472139250504213 which has three 1's.
355 is not in the sequence as it has exactly one 1. (End)

Mathematica

Select[Range[310], DigitCount[Fibonacci[#], 10, 1]==2&] (* Harvey P. Dale, Apr 02 2012 *)

Crossrefs

Cf. A000045, A085855 (number of 1's in decimal expansion of Fibonacci(n)).

Sequence in context: A390595 A129071 A066125 * A390820 A039342 A043165

Adjacent sequences: A181688 A181689 A181690 * A181692 A181693 A181694

Keyword

nonn,base

Author

Zak Seidov, Nov 05 2010

Status

approved