OFFSET

1,2

COMMENTS

Respectively, corresponding Fibonacci numbers are 1, 1, 2, 8, 144, 2584, 46368, 832040, 14930352, 267914296, 4807526976, 86267571272, 1548008755920, 498454011879264, 160500643816367088, 2880067194370816120, ...

Note that sequence does not contain all the positive multiples of 6, e.g., 66 and 102. See A335976 for a related sequence.

Conjecture: Sequence is infinite. - Altug Alkan, Jul 05 2020

All terms > 2 are multiples of 3, because Fibonacci(k) is odd unless k is a multiple of 3. Are all terms > 3 multiples of 6? If a term k is not a multiple of 6, then since Fibonacci(k) is not divisible by 4, Fibonacci(k)+1 must be in A114871. - Robert Israel, Aug 02 2020

EXAMPLE

12 is in the sequence because Fibonacci(12) = 144 is in A000010.

MAPLE

select(k -> numtheory:-invphi(combinat:-fibonacci(k))<>[], [1, 2, seq(i, i=3..100, 3)]); # Robert Israel, Aug 02 2020

PROG

(PARI) isok(k) = istotient(fibonacci(k)); \\ Altug Alkan, Jul 05 2020

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Jan 07 2017

EXTENSIONS

a(28)-a(49) from Jinyuan Wang, Jul 08 2020

STATUS

approved