

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(n1); a(1)=1 and a(2)=2.


3



1, 2, 6, 5, 12, 8, 21, 14, 18, 32, 15, 38, 24, 51, 28, 50, 23, 58, 36, 48, 13, 74, 62, 45, 60, 16, 92, 77, 34, 44, 11, 70, 122, 53, 142, 90, 108, 19, 182, 164, 40, 125, 86, 82, 96, 72, 25, 98, 150, 165, 54, 112, 59, 110, 52, 120, 69, 106, 78, 29, 102, 228, 127, 206, 80, 256, 177, 162
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OFFSET

1,2


COMMENTS

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


LINKS



FORMULA

a(534+(k+1)*3) = 2*a(534+k*3)1 for k >= 0 and a(534) = 555.
a(535+(k+1)*3) = 2*a(535+k*3)+1 for k >= 0 and a(535) = 2214.
a(536+(k+1)*3) = 2*a(536+k*3)+2 for k >= 0 and a(536) = 3322. (End)


EXAMPLE

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.


PROG

(MATLAB)
a = [1 2];
for n = 3:max_n
m = 1; d = abs(a(n1)a(n2));
while ~isempty(find(a==(m*(m+d)), 1))
m = m+1;
end
a(n) = m*(m+d);
end


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



