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A244280
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Denominators of the n-th iteration of the alternating continued fraction of the positive integers, initiated with (1 + ...).
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4
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2, 2, 11, 27, 202, 870, 8129, 50681, 570638, 4673558, 61724211, 627102091, 9514420518, 115483788186, 1980202320561, 27962630844865, 534877446987082, 8615820301234778, 181912525664114699, 3292162161484924619, 76056192127792619858, 1527880958525256735838
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OFFSET
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1,1
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COMMENTS
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As n-->inf, a(n) converges to 0.628736607098954801603428...
This is the result of taking the denominator of a continued fraction with alternating signs a(n) = 1/(1+1/(2-1/(3+1/(4-...1/(n +/- 1))))), where addition follows an odd number and subtraction follows an even number.
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..449
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EXAMPLE
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a(1) = 1/(1+1) = 1/2;
a(2) = 1/(1+1/(2-1)) = 1/2;
a(3) = 1/(1+1/(2-1/(3+1))) = 7/11;
a(4) = 1/(1+1/(2-1/(3+1/(4-1)))) = 17/27.
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MAPLE
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seq(denom(numtheory:-cfrac([0, [1, 1], seq([(-1)^j, j], j=2..n), [(-1)^(n+1), 1]])), n = 1..40); # Robert Israel, Jan 17 2016
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PROG
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(PARI) a(n) = if(n%2==0, s=-1, s=1); t=1; while(n>0, t=n+s/t; n--; s=-s); denominator(t=1/t)
vector(30, n, a(n)) \\ Colin Barker, Jul 20 2014
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CROSSREFS
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Cf. A244279 (Numerators).
Sequence in context: A175202 A187430 A151365 * A090527 A014220 A089544
Adjacent sequences: A244277 A244278 A244279 * A244281 A244282 A244283
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KEYWORD
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nonn,frac
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AUTHOR
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Mohamed Sabba, Jun 24 2014
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EXTENSIONS
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More terms from Colin Barker, Jul 20 2014
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STATUS
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approved
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