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%I #18 Feb 08 2023 11:17:25
%S 2,3,5,7,7,9,13,12,19,10,19,29,19,33,15,37,37,25,51,44,57,49,63,17,69,
%T 35,79,33,49,33,97,82,109,33,61,37,113,123,127,137,112,62,119,149,149,
%U 16,30,169,171,80,21,149,103,157,193,85
%N Number of distinct residues in the Fibonacci sequence mod the n-th prime.
%H Charles R Greathouse IV, <a href="/A137750/b137750.txt">Table of n, a(n) for n = 1..10000</a>
%H Casey Mongoven, <a href="http://caseymongoven.com/catalogue/b743.htm">Unique Residues Primes no. 1</a>; electro-acoustic music created with this sequence.
%F a(n) = A066853(A000040(n)). - _Max Alekseyev_, Feb 08 2023
%e The 5th prime number is 11. The Fibonacci sequence mod 11 is {0,1,1,2,3,5,8,2,10,1,0,1,...} - a periodic sequence. There are 7 distinct residues in this sequence, namely {0,1,2,3,5,8,10}. So a(5) = 7.
%t With[{f=Fibonacci[Range[500]]},Table[Length[Union[Mod[f,Prime[n]]]],{n,60}]] (* _Harvey P. Dale_, Aug 15 2012 *)
%o (PARI) a(n)=my(v=List([0,1]),p=prime(n));while(v[#v]||v[#v-1]!=1, listput(v,(v[#v]+v[#v-1])%p));#vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Apr 24 2012
%Y Cf. A066853, A137751, A000045, A001175.
%K nonn
%O 1,1
%A _Casey Mongoven_, Feb 10 2008
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