A077625 - OEIS

A077625

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

0, 2, 4, 6, 10, 14, 22, 30, 44, 62, 90, 126, 180, 254, 362, 510, 724, 1022, 1448, 2046, 2896, 4094, 5792, 8190, 11584, 16382, 23170, 32766, 46340, 65534, 92680, 131070, 185362, 262142, 370726, 524286, 741454, 1048574, 1482910, 2097150, 2965820, 4194302, 5931640

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OFFSET

1,2

COMMENTS

a(n) = 0 iff n = 1, as a consequence of Catalan's conjecture or Mihăilescu's theorem. - Bernard Schott, Apr 24 2022

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..80

Wikipedia, Catalan's conjecture.

MATHEMATICA

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

CROSSREFS

Cf. A077624-A077635.