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A232357 The number of pairs of numbers below n that, when generating a Fibonacci-like sequence modulo n, do not contain zero. 2
0, 0, 0, 0, 4, 0, 0, 24, 0, 16, 20, 48, 84, 0, 36, 120, 144, 144, 36, 64, 288, 80, 0, 360, 104, 336, 0, 288, 448, 144, 60, 504, 580, 864, 196, 912, 684, 792, 756, 760, 880, 1152, 0, 920, 324, 1056, 1472, 1800, 0, 416, 1296, 1344, 1404, 1440, 2504, 2040, 1620, 1792, 116, 1584, 2820, 2040, 2880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n) = 0 iff n is in A064414, a(n) is not equal to zero iff n is in A230457.

a(n) + A232656(n) = n^2.

LINKS

Table of n, a(n) for n=1..63.

B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.8.5.

EXAMPLE

The sequence 2,1,3,4,2,1 is the sequence of Lucas numbers modulo 5. Lucas numbers are never divisible by 5. The 4 pairs (2,1), (1,3), (3,4), (4,2) are the only pairs that can generate a sequence modulo 5 that doesn't contain zeros. Thus, a(5) = 4.

Any Fibonacci like sequence contains elements divisible by 2, 3, or 4. Thus, a(2) = a(3) = a(4) = 0.

MATHEMATICA

fibLike[list_] := Append[list, list[[-1]] + list[[-2]]]; Table[Count[Flatten[Table[Count[Nest[fibLike, {n, m}, k^2]/k, _Integer], {n, k-1}, {m, k-1}]], 0], {k, 70}]

CROSSREFS

Cf. A064414, A230457, A232656.

Sequence in context: A125762 A286216 A280727 * A196302 A307186 A060784

Adjacent sequences:  A232354 A232355 A232356 * A232358 A232359 A232360

KEYWORD

nonn

AUTHOR

Brandon Avila and Tanya Khovanova, Nov 22 2013

STATUS

approved

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Last modified April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)