A272355 Numbers of the form Fibonacci(12n)/(144n).

1, 161, 34561, 8346401, 2150012161, 576914365601, 44861726436508961, 12840299190293644801, 3721082815965949056161, 321507757074243457409731361, 28572486227889263832443550935201, 8586901708088882505643582648796161

Offset: 1

Author

Peter M. Chema, Apr 29 2016

Keywords

• nonn
• easy

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.

Examples

			a(3) = Fib(12*3)/(144*3) = Fib36 / 432 = 34561; therefore, the third term is the integer 34561.
		

Crossrefs

Cf. A072378.

Programs

Mathematica

Select[Table[Fibonacci[12n]/(144n),{n,20}],IntegerQ] (* Harvey P. Dale, Sep 26 2016 *)

PARI

for(n=1,100, t=fibonacci(12*n)/144/n; if(denominator(t)==1, print1(t", "))) \\ Charles R Greathouse IV, Apr 30 2016

Formula

a(n) = Integer Values of Fib(12n)/(144n)