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 A145300 a(n) is the maximal prime such that if p_n is the n-th prime then (ceiling(sqrt(a(n)*p_n)))^2-a(n)*p_n is a perfect square 2
 2, 7, 13, 13, 19, 23, 29, 31, 37, 43, 47, 53, 61, 61, 67, 73, 79, 83, 89, 89, 97, 103, 109, 113, 113, 131, 131, 137, 139, 139, 157, 163, 167, 173, 181, 181, 193, 199, 199, 211, 211, 211, 229, 233, 233, 239, 251, 263, 271, 271, 277, 283, 283, 293, 293, 307, 317, 317, 317, 317 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Theorem. a(n)<=p_n+2sqrt(2p_n)+2. For example, for n=25, p_n=97. Using the theorem, we find: a(25)<=126. Now, by the definition of the sequence, we verify that a(25)=113. Or a(n) is the maximal prime q_n>p_n such that sqrt(q_n)-sqrt(p_n)

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Last modified July 11 14:11 EDT 2020. Contains 335626 sequences. (Running on oeis4.)