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A205113 Least k such that n divides the k-th difference between distinct Lucas numbers.

%I A205113 #11 Feb 25 2024 02:10:35
%S A205113 1,1,2,5,7,4,9,8,20,7,14,26,17,13,12,41,11,20,44,25,42,19,22,31,18,17,
%T A205113 113,16,27,38,119,49,46,52,42,26,68,44,48,25,54,80,24,23,59,22,35,49,
%U A205113 47,109,71,67,58,113,63,41,132,34,87,38
%N A205113 Least k such that n divides the k-th difference between distinct Lucas numbers.
%C A205113 The pairs of Lucas numbers are ordered as at A205112.  For a guide to related sequences, see A204892.
%H A205113 Robert Israel, <a href="/A205113/b205113.txt">Table of n, a(n) for n = 1..10000</a>
%p A205113 N:= 100: # to get terms before the first term > N*(N-1)/2
%p A205113 L:= proc(n) option remember; combinat:-fibonacci(n+1)+combinat:-fibonacci(n-1); end proc:
%p A205113 A205112:= [seq(seq(L(j)-L(i),i=1..j-1),j=2..N)]:
%p A205113 M:= N*(N-1)/2:
%p A205113 f:= proc(n) local k;
%p A205113   for k from 1 to M do if A205112[k] mod n = 0 then return k fi od;
%p A205113   -1
%p A205113 end proc:
%p A205113 R:= NULL:
%p A205113 for n from 1 do
%p A205113 v:= f(n);
%p A205113 if v = -1 then break fi;
%p A205113 R:= R,v
%p A205113 od:
%p A205113 R; # _Robert Israel_, Feb 25 2024
%t A205113 (See the program at A205114.)
%Y A205113 Cf. A205114, A204892.
%K A205113 nonn,look
%O A205113 1,3
%A A205113 _Clark Kimberling_, Jan 22 2012