A205113 - OEIS

%I #11 Feb 25 2024 02:10:35

%S 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 113,16,27,38,119,49,46,52,42,26,68,44,48,25,54,80,24,23,59,22,35,49,

%U 47,109,71,67,58,113,63,41,132,34,87,38

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

%C The pairs of Lucas numbers are ordered as at A205112.  For a guide to related sequences, see A204892.

%H Robert Israel, <a href="/A205113/b205113.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 100: # to get terms before the first term > N*(N-1)/2

%p L:= proc(n) option remember; combinat:-fibonacci(n+1)+combinat:-fibonacci(n-1); end proc:

%p A205112:= [seq(seq(L(j)-L(i),i=1..j-1),j=2..N)]:

%p M:= N*(N-1)/2:

%p f:= proc(n) local k;

%p   for k from 1 to M do if A205112[k] mod n = 0 then return k fi od;

%p   -1

%p end proc:

%p R:= NULL:

%p for n from 1 do

%p v:= f(n);

%p if v = -1 then break fi;

%p R:= R,v

%p od:

%p R; # _Robert Israel_, Feb 25 2024

%t (See the program at A205114.)

%Y Cf. A205114, A204892.

%K nonn,look

%O 1,3

%A _Clark Kimberling_, Jan 22 2012