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A213277 a(n) is the length of the cycle of first differences of k such that Fibonacci(k) mod n = k mod n. 2
3, 8, 3, 8, 6, 16, 3, 8, 14, 10, 4, 28, 24, 16, 3, 36, 6, 18, 11, 16, 15, 48, 3, 18, 42, 8, 12, 14, 14, 30, 3, 40, 18, 32, 4, 76, 9, 56, 11, 40, 12, 88, 15, 16, 24, 32, 3, 16, 34, 24, 21, 108, 6, 8, 6, 24, 21, 58, 12, 60, 15, 16, 3, 56, 30, 136, 9, 16, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

In calculating the terms, a set of values A that is found twice (AA) is not enough to be certain that A is a cycle since the continuation may be AAA..AAABAAA..AAAB where B is a different set of values. In calculating the data above, a cycle is accepted when it has occurred 10 times in a row.

LINKS

Lars Blomberg, Table of n, a(n) for n = 2..23002

EXAMPLE

Example with n=3:

Fib(k): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368,...

Fib(k) mod 3: 0,1,1,2,0,2,2,1,0,1,1,2,0,2,2,1,0,1,1,2,0,2,2,1,0

k mod 3:      0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0

Accepted k values indicated by x:

              x,x,-,-,-,x,-,x,-,-,x,x,x,-,-,-,-,-,-,-,-,-,-,-,x

Accepted k values: 0, 1, 5, 7, 10, 11, 12, 14, 24

First differences of k values: 1, 4, 2, 3, 1, 1, 2, 10

After this the cycle repeats, so a(3) = 8.

CROSSREFS

Cf. A000045, A213278.

Sequence in context: A125025 A204998 A019919 * A135608 A106230 A205126

Adjacent sequences:  A213274 A213275 A213276 * A213278 A213279 A213280

KEYWORD

nonn

AUTHOR

Lars Blomberg, Jun 08 2012

STATUS

approved

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Last modified April 3 21:54 EDT 2020. Contains 333207 sequences. (Running on oeis4.)