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A359035 a(n+1) is the smallest number not already used which can be written as the product of two numbers with the same difference as a(n) and a(n-1); a(1)=1 and a(2)=2.

%I A359035 #25 Apr 09 2023 15:31:31
%S A359035 1,2,6,5,12,8,21,14,18,32,15,38,24,51,28,50,23,58,36,48,13,74,62,45,
%T A359035 60,16,92,77,34,44,11,70,122,53,142,90,108,19,182,164,40,125,86,82,96,
%U A359035 72,25,98,150,165,54,112,59,110,52,120,69,106,78,29,102,228,127,206,80,256,177,162
%N A359035 a(n+1) is the smallest number not already used which can be written as the product of two numbers with the same difference as a(n) and a(n-1); a(1)=1 and a(2)=2.
%C A359035 This sequence starts chaotic but makes a sudden transition into a linear recurrence for n > 433. For details see the formula section. - _Thomas Scheuerle_, Dec 13 2022
%H A359035 Neal Gersh Tolunsky, <a href="/A359035/b359035.txt">Table of n, a(n) for n = 1..600</a>
%H A359035 Thomas Scheuerle, <a href="/A359035/a359035.png">Scatter plot log(a(n)) for n = 1...650</a>
%F A359035 From _Thomas Scheuerle_, Dec 13 2022: (Start)
%F A359035 a(534+(k+1)*3) = 2*a(534+k*3)-1 for k >= 0 and a(534) = 555.
%F A359035 a(535+(k+1)*3) = 2*a(535+k*3)+1 for k >= 0 and a(535) = 2214.
%F A359035 a(536+(k+1)*3) = 2*a(536+k*3)+2 for k >= 0 and a(536) = 3322. (End)
%e A359035 a(3) is 6: The difference between the two previous terms is 1 and 2*3=6 is the smallest number that is the product of two numbers with a difference of 1.
%o A359035 (MATLAB)
%o A359035 function a = A359035( max_n )
%o A359035     a = [1 2];
%o A359035     for n = 3:max_n
%o A359035         m = 1; d = abs(a(n-1)-a(n-2));
%o A359035         while ~isempty(find(a==(m*(m+d)), 1))
%o A359035             m = m+1;
%o A359035         end
%o A359035         a(n) = m*(m+d);
%o A359035     end
%o A359035 end % _Thomas Scheuerle_, Dec 13 2022
%Y A359035 Cf. A002378.
%K A359035 nonn
%O A359035 1,2
%A A359035 _Neal Gersh Tolunsky_, Dec 12 2022