

A166074


a(n)=n*n  [biggest Fibonacci number <= n*n]


0



0, 1, 1, 3, 4, 2, 15, 9, 26, 11, 32, 0, 25, 52, 81, 23, 56, 91, 128, 23, 64, 107, 152, 199, 15, 66, 119, 174, 231, 290, 351, 37, 102, 169, 238, 309, 382, 457, 534, 3, 84, 167, 252, 339, 428, 519, 612, 707, 804, 903, 17, 120, 225, 332, 441, 552, 665, 780, 897, 1016, 1137
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OFFSET

1,4


COMMENTS

The only numbers n where a(n)=0 are 1 and 12, a(1)=1*11 =0 and a(12)=12*12144=0. Cohn (1964) proved 1 and 144 are the only Fibonacci numbers which are perfect squares. In general how many Fibonacci numbers there exist for a positive integer k such that k = n*n(biggest Fib. number <= n*n). The only proved answer is 2 for k=0.


LINKS

Table of n, a(n) for n=1..61.
J. H. E. Cohn, On square Fibonacci numbers, Journal London Math.Soc., 39 (1964), p.537540.


CROSSREFS

Cf. A000045
Sequence in context: A159672 A059114 A246322 * A225475 A259334 A210488
Adjacent sequences: A166071 A166072 A166073 * A166075 A166076 A166077


KEYWORD

easy,nonn


AUTHOR

Ctibor O. Zizka, Oct 06 2009


EXTENSIONS

a(7) corrected and more terms appended by R. J. Mathar, Oct 08 2009


STATUS

approved



