Fibonacci numbers

A number in the sequence defined by the recurrence F(1)=F(2)=1 and F(n)=F(n-1)+F(n-2). more

The Fibonacci numbers up to 10¹⁵ :

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 72 values, from 1 to 806515533049393).

n\r	0	1
2	24	48	2
3	18	27	27	3
4	12	36	12	12	4
5	14	14	13	16	15	5
6	6	18	9	12	9	18	6
7	9	18	9	5	4	9	18	7
8	12	18	12	6	0	18	0	6	8
9	6	15	6	6	6	6	6	6	15	9
10	4	10	5	11	6	10	4	8	5	9	10
11	7	22	15	7	0	7	0	0	7	0	7

A pictorial representation of the table above

Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.

e-mail: info -at- numbersaplenty.com • Privacy notice • engine limits

n\r	0	1
2	24	48	2
3	18	27	27	3
4	12	36	12	12	4
5	14	14	13	16	15	5
6	6	18	9	12	9	18	6
7	9	18	9	5	4	9	18	7
8	12	18	12	6	0	18	0	6	8
9	6	15	6	6	6	6	6	6	15	9
10	4	10	5	11	6	10	4	8	5	9	10
11	7	22	15	7	0	7	0	0	7	0	7

n\r	0	1
2	24	48	2
3	18	27	27	3
4	12	36	12	12	4
5	14	14	13	16	15	5
6	6	18	9	12	9	18	6
7	9	18	9	5	4	9	18	7
8	12	18	12	6	0	18	0	6	8
9	6	15	6	6	6	6	6	6	15	9
10	4	10	5	11	6	10	4	8	5	9	10
11	7	22	15	7	0	7	0	0	7	0	7

n\r	0	1
2	24	48	2
3	18	27	27	3
4	12	36	12	12	4
5	14	14	13	16	15	5
6	6	18	9	12	9	18	6
7	9	18	9	5	4	9	18	7
8	12	18	12	6	0	18	0	6	8
9	6	15	6	6	6	6	6	6	15	9
10	4	10	5	11	6	10	4	8	5	9	10
11	7	22	15	7	0	7	0	0	7	0	7