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 A223139 Decimal expansion of (sqrt(13) - 1)/2. 4
 1, 3, 0, 2, 7, 7, 5, 6, 3, 7, 7, 3, 1, 9, 9, 4, 6, 4, 6, 5, 5, 9, 6, 1, 0, 6, 3, 3, 7, 3, 5, 2, 4, 7, 9, 7, 3, 1, 2, 5, 6, 4, 8, 2, 8, 6, 9, 2, 2, 6, 2, 3, 1, 0, 6, 3, 5, 5, 2, 2, 6, 5, 2, 8, 1, 1, 3, 5, 8, 3, 4, 7, 4, 1, 4, 6, 5, 0, 5, 2, 2, 2, 6, 0, 2, 3, 0, 9, 5, 4, 1, 0, 0, 9, 2, 4, 5, 3, 5, 8, 8, 3, 6, 7, 5, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Apart from a(1) the same as A209927 and A085550. [Joerg Arndt, Sep 17 2013] Decimal expansion of sqrt(3 - sqrt(3 - sqrt(3 - sqrt(3 - ... )))). Sequence with a(1) = 2 is decimal expansion of sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + ... )))) - A209927. This is the positive root of x^2 + x - 3, and the negative one is -A209927. - Wolfdieter Lang, Aug 29 2022 LINKS Table of n, a(n) for n=1..106. B. Sury, Nothing Lucky about 13, Mathematics Magazine, Vol. 83, No. 4 (October 2010), pp. 289-293. FORMULA Closed form: (sqrt(13) - 1)/2 = A209927-1 = A098316-2. sqrt(3 - sqrt(3 - sqrt(3 - sqrt(3 - ... )))) + 1 = sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + ... )))). See A209927. Equals 2*(cos(2*Pi/13) + cos(6*Pi/13) + cos(8*Pi/13)) (see Sury link). - Michel Marcus, Aug 21 2015 EXAMPLE 1.3027756377319946465... MATHEMATICA RealDigits[(Sqrt[13] - 1)/2, 10, 130] PROG (PARI) (sqrt(13)-1)/2 \\ Altug Alkan, Oct 02 2018 CROSSREFS Cf. A098316, A209927, A085550, A209927. CF. A122553 (continued fraction). Sequence in context: A011075 A248820 A085550 * A302278 A302728 A302528 Adjacent sequences: A223136 A223137 A223138 * A223140 A223141 A223142 KEYWORD nonn,cons,easy AUTHOR Jaroslav Krizek, Apr 02 2013 STATUS approved

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Last modified February 28 07:05 EST 2024. Contains 370387 sequences. (Running on oeis4.)