A002794 Numerators of convergents to Lehmer's constant.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• nice

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

• 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

Crossrefs

Cf. A002795, A002665, A030125, A002065.

Programs

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 *)