

A330712


Numbers k such that F(k)  1 is divisible by floor((k  1)/2), where F(k) is the kth Fibonacci number (A000045).


1



3, 4, 5, 7, 15, 22, 25, 26, 27, 35, 41, 47, 49, 50, 73, 74, 75, 87, 89, 95, 97, 98, 101, 107, 121, 122, 135, 145, 146, 147, 167, 193, 194, 195, 207, 215, 217, 218, 221, 227, 241, 242, 255, 275, 289, 290, 315, 327, 335, 337, 338, 347, 361, 362, 385, 386, 387, 395
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OFFSET

1,1


COMMENTS

Numbers of the form F(k)  1 have the same Zeckendorf (A014417) and dual Zeckendorf (A104326) representations: alternating digits of 1 and 0 whose sum is floor((k  1)/2). Thus, if k is in this sequence then F(k)  1 is both a ZeckendorfNiven number (A328208) and a lazyFibonacciNiven number (A328212), i.e., A000071(a(n)) is in A330711.


LINKS



EXAMPLE

7 is in this sequence since F(7)  1 = 13  1 = 12 is divisible by floor((7  1)/2) = 3. The Zeckendorf and dual Zeckendorf representations of 7 are both 1010, whose sum of digits, 2, divides 12. Thus 12 is both a ZeckendorfNiven number and a lazyFibonacciNiven number.


MATHEMATICA

Select[Range[3, 400], Divisible[Fibonacci[#]  1, Floor[(#  1)/2]] &]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



