A077624 Largest term in periodic part of continued fraction expansion of square root of 2^n + 1 or 0 if 2^n + 1 is a square.

2, 4, 0, 8, 10, 16, 22, 32, 44, 64, 90, 128, 180, 256, 362, 512, 724, 1024, 1448, 2048, 2896, 4096, 5792, 8192, 11584, 16384, 23170, 32768, 46340, 65536, 92680, 131072, 185362, 262144, 370726, 524288, 741454, 1048576, 1482910, 2097152, 2965820, 4194304, 5931640

Offset: 1

Author

Labos Elemer, Nov 13 2002

Keywords

• nonn

Comments

a(n) = 0 iff n = 3, as a consequence of Catalan's conjecture or Mihăilescu's theorem. - Bernard Schott, Apr 22 2022

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..78
• Wikipedia, Catalan's conjecture.

Crossrefs

Cf. A077625-A077635.

Programs

Mathematica

Table[Max[Last[ContinuedFraction[Sqrt[1+2^u]]]], {u, 1, 32}]

Extensions

Definition clarified, a(3) corrected and a(33)-a(43) added by Chai Wah Wu, Apr 19 2022