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A084334 a(1) = 1; a(n+1) is the least squarefree m not already used such that |m-a(n)| is not equal to |a(k+1)-a(k)| for any k < n.

%I A084334 #13 Feb 22 2024 20:21:20
%S A084334 1,2,5,3,7,13,6,11,19,10,21,31,14,26,39,15,29,47,17,33,53,22,37,58,23,
%T A084334 42,65,38,66,30,55,77,34,67,35,61,95,41,70,107,43,82,122,46,87,129,51,
%U A084334 89,133,59,105,57,102,149,62,111,161,69,127,71,123,174,73,130,183,74
%N A084334 a(1) = 1; a(n+1) is the least squarefree m not already used such that |m-a(n)| is not equal to |a(k+1)-a(k)| for any k < n.
%H A084334 Robert Israel, <a href="/A084334/b084334.txt">Table of n, a(n) for n = 1..10000</a>
%p A084334 N:= 1000: # for terms before the first term > N
%p A084334 A[1]:= 1:
%p A084334 SF:= select(numtheory:-issqrfree, [$2..N]):
%p A084334 DA:= {}:
%p A084334 y:= 1:
%p A084334 found:= true:
%p A084334 for n from 2 while found do
%p A084334   found:= false;
%p A084334   for j from 1 to nops(SF) while not found do
%p A084334     x:= SF[j];
%p A084334     if not member(abs(x-y),DA) then
%p A084334        found:= true;
%p A084334        A[n]:= x;
%p A084334        DA:= DA union {abs(x-y)};
%p A084334        SF:= subsop(j=NULL, SF);
%p A084334        y:= x;
%p A084334     fi
%p A084334 od od:
%p A084334 convert(A,list); # _Robert Israel_, Feb 22 2024
%Y A084334 Cf. A081145, A084331.
%K A084334 nonn,easy
%O A084334 1,2
%A A084334 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 18 2003
%E A084334 Edited and extended by _David Wasserman_, Dec 15 2004