A085855 -id:A085855 - cp's OEIS frontend

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

Zak Seidov, Nov 05 2010

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)

			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)

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

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

cp's OEIS Frontend

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

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