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 A319016 Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)). 2
 1, 2, 6, 5, 8, 7, 0, 0, 9, 5, 2, 3, 0, 8, 6, 6, 3, 6, 8, 4, 1, 8, 9, 2, 1, 3, 1, 4, 5, 4, 3, 5, 4, 3, 4, 2, 7, 4, 6, 4, 2, 6, 5, 4, 4, 6, 3, 9, 9, 6, 3, 8, 7, 1, 6, 8, 2, 0, 0, 5, 3, 3, 4, 1, 8, 1, 4, 8, 9, 3, 4, 9, 2, 5, 1, 1, 2, 7, 4, 8, 9, 4, 4, 3, 7, 0, 6, 4, 5, 9, 7, 4, 8, 3, 5, 3, 0, 5, 6, 7, 3, 9, 0, 8, 4, 2, 7, 1, 1, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The binary expansion is the characteristic function of the oblong numbers (A005369). The Engel expansion of this constant are the powers of 4 (A000302). - Amiram Eldar, Dec 07 2020 LINKS Table of n, a(n) for n=1..110. FORMULA Equals theta_2(1/2)/2^(3/4), where theta_2 is the Jacobi theta function. EXAMPLE 1.2658700952308663684189... = (1.010001000001000000010000000001...)_2. | | | | | | 0 2 6 12 20 30 MATHEMATICA RealDigits[EllipticTheta[2, 0, 1/2]/2^(3/4), 10, 110] [[1]] PROG (PARI) suminf(k=0, 1/2^(k*(k+1))) \\ Michel Marcus, Sep 08 2018 CROSSREFS Cf. A000302, A002378, A005369, A053763, A190405, A299998, A319015. Sequence in context: A175293 A021083 A244928 * A262096 A011043 A021380 Adjacent sequences: A319013 A319014 A319015 * A319017 A319018 A319019 KEYWORD nonn,cons AUTHOR Ilya Gutkovskiy, Sep 07 2018 STATUS approved

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Last modified August 15 04:38 EDT 2024. Contains 375172 sequences. (Running on oeis4.)