First sequence with no square differences
Ruby, 72 62 57 50 47 bytes

0.step{|x|$*&lt;&lt;p(x)if$*.all?{|i|(x-i)**0.5%1&gt;0}}

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Prints all terms of the sequence indefinitely.
7 bytes saved by Dingus and further 3 by Sisyphus.
Ruby 2.7+, 45 bytes

0.step{|x|$*&lt;&lt;p(x)if$*.all?{(x-_1)**0.5%1&gt;0}}