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 A263295 Denominators of the n-th iteration of the alternating continued fraction formed from the positive integers, starting with (1 - ...). 3
 3, 5, 33, 111, 933, 4913, 50585, 364717, 4460647, 40920133, 580574377, 6472209467, 104581586665, 1373040648769, 24902871413201, 376386726269561, 7573128424949291, 129519388933667493, 2863373356440803473, 54670305859684290279, 1317404009250178503245 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS As n->inf, A262957(n)/a(n) converges to 0.57663338973018...; this number has a surprisingly elegant standard continued fraction representation: [0; 1, 1, 2, 1, 3, 4, 1, 5, 6, 1, 7, 8, ...]. LINKS Jinyuan Wang, Table of n, a(n) for n = 1..448 EXAMPLE (1-1/(2+1)) = 2/3, so a(1) = 3; (1-1/(2+1/(3-1))) = 3/5, so a(2) = 5; (1-1/(2+1/(3-1/(4+1)))) = 19/33, so a(3) = 33; (1-1/(2+1/(3-1/(4+1/(5-1))))) = 64/111, so a(4) = 111. PROG (PARI) a(n) = if(n%2==0, s=-1, s=1); t=1; while(n>0, t=n+1+s/t; n--; s=-s); denominator(t=1/t) vector(30, n, a(n)) \\ corrected by Mohammed Sabba, Dec 22 2015 CROSSREFS Same principle as A244279 and A244280 - except here we begin with subtraction rather than addition. Cf. A262957 (numerators). Sequence in context: A103010 A225866 A332704 * A222484 A354849 A222630 Adjacent sequences: A263292 A263293 A263294 * A263296 A263297 A263298 KEYWORD nonn,frac AUTHOR Mohamed Sabba, Nov 20 2015 EXTENSIONS More terms from Mohamed Sabba, Dec 22 2015 STATUS approved

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Last modified July 16 10:27 EDT 2024. Contains 374345 sequences. (Running on oeis4.)