A002794 Numerators of convergents to Lehmer's constant. (Formerly M3034 N1230)

1, 1, 3, 16, 547, 538811, 620245817465, 692770666469127829226736, 1025344764595988314871439243086711931108916434521

Offset

0,3

References

D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

J. W. Wrench, Jr., personal communication.

Links

Table of n, a(n) for n=0..8.

D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340. [Annotated scanned copy]

J. W. Wrench, Jr., Letters to N. J. A. Sloane, Feb 1974

Mathematica

Block[{$MaxExtraPrecision=1000}, Numerator[Convergents[With[{nn=15}, Cot[ Total[Last[#] ArcCot[First[#]]&/@Thread[{NestList[#^2+#+1&, 0, nn], PadRight[{}, nn+1, {1, -1}]}]]]], 10]]] (* Harvey P. Dale, Jan 29 2012 *)

Crossrefs

Cf. A002794, A002795, A002665, A030125, A002065.

Sequence in context: A081780 A362382 A297118 * A132559 A304761 A316507

Adjacent sequences: A002791 A002792 A002793 * A002795 A002796 A002797

Keyword

nonn,frac,nice

Author

N. J. A. Sloane

Status

approved