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A006271 Numerators of a continued fraction for 1 + sqrt(2).
(Formerly M1555)
1
2, 5, 197, 7761797, 467613464999866416197, 102249460387306384473056172738577521087843948916391508591105797 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

With b(n) = floor((1+sqrt(2))^n) (cf. A080039) the terms appear to be b(2*3^n). - Joerg Arndt, Apr 29 2013

Note that 1 + sqrt(2) = (c + sqrt(c^2+4))/2 and has regular continued fraction [c, c, ...] with c = 2. With b(n) = A006266(n), it can be expanded into an irregular continued fraction f(1) = b(1) and f(n) = (b[n-1]^2+1)/(b[n]-b[n-1]), and numerator(f(n)) = a(n) (cf. Shallit). - Michel Marcus, Apr 29 2013

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..5.

Jeffrey Shallit, Predictable regular continued cotangent expansions, J. Res. Nat. Bur. Standards Sect. B 80B (1976), no. 2, 285-290.

CROSSREFS

For denominators see A006272.

Sequence in context: A100366 A012975 A012954 * A013105 A208210 A216458

Adjacent sequences:  A006268 A006269 A006270 * A006272 A006273 A006274

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Previous values for a(3) and a(4) were 776 and 1797. They have been merged into 7761797 to reflect the 2nd continued fraction on page 6 of Shallit paper by Michel Marcus, Apr 29 2013

STATUS

approved

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Last modified February 23 12:03 EST 2019. Contains 320431 sequences. (Running on oeis4.)