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%I #11 Jun 26 2018 06:36:12
%S 1,2,3,4,6,5,7,8,9,12,10,11,13,14,17,16,15,21,18,19,23,20,22,25,24,26,
%T 27,28,29,37,30,31,33,32,34,35,36,38,39,43,40,41,42,44,47,45,46,53,48,
%U 49,51,50,52,55,54,59,57,56,58,67,60,61,63,62,64,65,66,68,69,72,70,71
%N a(n) = the smallest positive integer which does not occur earlier in the sequence and which is coprime to the n-th Fibonacci number.
%C Sequence is a permutation of the positive integers.
%H Robert Israel, <a href="/A121730/b121730.txt">Table of n, a(n) for n = 1..10000</a>
%e 55 is the 10th Fibonacci number. Among those positive integers not occurring among the first 9 terms of the sequence, 12 is the smallest which is coprime to 55, so a(10) = 12. 10 and 11 also do not occur among the first 9 terms of the sequence, but they are not coprime to 55.
%p L:= [$1..100]: # for all terms before the first term > 100
%p for n from 1 do
%p v:= combinat:-fibonacci(n);
%p found:= false;
%p for j from 1 to nops(L) do
%p if igcd(L[j],v)=1 then
%p A[n]:= L[j];
%p L:= subsop(j=NULL,L);
%p found:= true;
%p break
%p fi;
%p od;
%p if not found then break fi
%p od:
%p seq(A[i],i=1..n-1); # _Robert Israel_, Jun 26 2018
%Y Cf. A000045, A121731.
%K nonn
%O 1,2
%A _Leroy Quet_, Aug 18 2006
%E Extended by _Ray Chandler_, Aug 22 2006
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