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 A081794 Continued cotangent for Pi/4. 0
 0, 1, 8, 211, 114681, 118304381067, 14093169772574392414247, 233069007722838136376547872705625127588988391, 148096265277934997326846757550268707006396575812305676278686643630022889932579135326452726 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340. LINKS Table of n, a(n) for n=0..8. FORMULA Pi/4=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=Pi/4, b(n)=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)) then a(n)=floor(b(n)) PROG (PARI) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=Pi/4; ?for(n=2, 10, bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)))) ?a(n)=floor(b(n+1)) CROSSREFS Cf. A002666, A002667, A002668. Sequence in context: A197980 A197767 A024288 * A221042 A358211 A247032 Adjacent sequences: A081791 A081792 A081793 * A081795 A081796 A081797 KEYWORD nonn AUTHOR Benoit Cloitre, Apr 10 2003 STATUS approved

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Last modified August 8 18:48 EDT 2024. Contains 375023 sequences. (Running on oeis4.)