The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)