|
|
A272355
|
|
Numbers of the form Fibonacci(12n)/(144n).
|
|
0
|
|
|
1, 161, 34561, 8346401, 2150012161, 576914365601, 44861726436508961, 12840299190293644801, 3721082815965949056161, 321507757074243457409731361, 28572486227889263832443550935201, 8586901708088882505643582648796161
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
The last two digits end either in 01 or 61. Digital root alternates 1 and 8.
Consecutive terms have ratios that approximate the product of Golden Ratio powers of multiples of 12 and consecutive integers fractions: E.g., the 4th term divided by the 3rd term approximates Golden Ratio^12 * 3/4; the 10th term divided by the 9th term approximates Golden Ratio^24 * 5/6; and the 16th term divided by the 15 term is a close approximation of Golden Ratio^48 * 5/6, etc.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Integer Values of Fib(12n)/(144n)
|
|
EXAMPLE
|
a(3) = Fib(12*3)/(144*3) = Fib36 / 432 = 34561; therefore, the third term is integer 34561.
|
|
MATHEMATICA
|
Select[Table[Fibonacci[12n]/(144n), {n, 20}], IntegerQ] (* Harvey P. Dale, Sep 26 2016 *)
|
|
PROG
|
(PARI) for(n=1, 100, t=fibonacci(12*n)/144/n; if(denominator(t)==1, print1(t", "))) \\ Charles R Greathouse IV, Apr 30 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|