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 A299118 Squares s such that prime(s) + 2 is a square. 0
 1, 4, 9, 7745089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Primes corresponding to the first four squares are 2, 7, 23, and 136866599. The sequence may be finite. There may be no square s such that prime(s) + 1 is square (none was found up to 10^9). This is a Diophantine problem of the form f(n^2) + A = m^2, where f(x) = prime(x), and the simplest case of A = 1 has probably no solutions unlike the same case with f(x) = primepi(x) that may even have an infinite number of solutions. LINKS EXAMPLE prime(4) + 2 = 7 + 2 = 9, and both 4 and 9 are squares. MATHEMATICA Select[Range[10^4]^2, IntegerQ@Sqrt[Prime[#] + 2] &] PROG (PARI) for(n=1, 10^4, issquare(prime(n^2)+2)&&print1(n^2 ", ")) CROSSREFS Cf. A000290 (squares), A000040 (primes), A011757 (primes with square indices). Sequence in context: A260305 A229338 A111443 * A276272 A331450 A051499 Adjacent sequences:  A299115 A299116 A299117 * A299119 A299120 A299121 KEYWORD nonn,more AUTHOR Waldemar Puszkarz, Feb 02 2018 STATUS approved

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Last modified August 5 19:40 EDT 2021. Contains 346488 sequences. (Running on oeis4.)