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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The only numbers n where a(n)=0 are 1 and 12, a(1)=1*1-1 =0 and a(12)=12*12-144=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.537-540.

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

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Last modified March 28 07:54 EDT 2017. Contains 284182 sequences.