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 A067874 Positive integers x satisfying x^2 - D*y^2 = 1 for a unique integer D. 6
 2, 4, 6, 12, 14, 16, 18, 20, 22, 30, 32, 34, 36, 38, 40, 42, 52, 54, 56, 58, 60, 66, 68, 70, 72, 78, 84, 86, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 112, 114, 128, 130, 132, 138, 140, 142, 144, 150, 156, 158, 160, 162, 164, 166, 178, 180, 182, 184, 186, 192, 194, 196, 198 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS D is unique iff x^2 - 1 is squarefree, in which case it follows with necessity that D=x^2-1 and y=1. All terms are even. A014574 is a subsequence. Conjecture: All terms of A002110 > 1 are a subsequence. - Griffin N. Macris, Apr 11 2016 All n such that n+1 and n-1 are in A056911. - Robert Israel, Apr 12 2016 Numbers with a squarefree neighbor. - Juri-Stepan Gerasimov, Jan 17 2017 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA a(n) = 2*A272799(n). - Juri-Stepan Gerasimov, Jan 17 2017. MAPLE select(t -> numtheory:-issqrfree(t^2-1), [seq(n, n=2..1000, 2)]); # Robert Israel, Apr 12 2016 MATHEMATICA Select[Range[200], SquareFreeQ[#^2-1]&] (* Vladimir Joseph Stephan Orlovsky, Oct 26 2009 *) PROG (MAGMA) [n: n in [1..110] | IsSquarefree(n-1) and IsSquarefree(n+1)]; \\ Juri-Stepan Gerasimov, Jan 17 2017 CROSSREFS Cf. A002110, A005117, A014574, A056911, A226993, A272799, A280892. Sequence in context: A062856 A056371 A271822 * A015733 A247460 A023187 Adjacent sequences:  A067871 A067872 A067873 * A067875 A067876 A067877 KEYWORD nice,nonn AUTHOR Lekraj Beedassy, Feb 25 2002 EXTENSIONS Corrected and extended by Max Alekseyev, Apr 26 2009 Further edited by Max Alekseyev, Apr 28 2009 STATUS approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)