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 A190405 Decimal expansion of Sum_{k>=1} (1/2)^T(k), where T=A000217 (triangular numbers); based on column 1 of the natural number array, A000027. 8
 6, 4, 1, 6, 3, 2, 5, 6, 0, 6, 5, 5, 1, 5, 3, 8, 6, 6, 2, 9, 3, 8, 4, 2, 7, 7, 0, 2, 2, 5, 4, 2, 9, 4, 3, 4, 2, 2, 6, 0, 6, 1, 5, 3, 7, 9, 5, 6, 7, 3, 9, 7, 4, 7, 8, 0, 4, 6, 5, 1, 6, 2, 2, 3, 8, 0, 1, 4, 4, 6, 0, 3, 7, 3, 3, 3, 5, 1, 7, 7, 5, 6, 0, 0, 3, 6, 4, 1, 7, 1, 6, 2, 3, 3, 5, 9, 1, 3, 3, 0, 8, 6, 0, 8, 9, 7, 3, 5, 3, 1, 6, 3, 4, 3, 6, 1, 9, 4, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A190404. Binary expansion is .1010010001... (A023531). - Rick L. Shepherd, Jan 05 2014 LINKS Danny Rorabaugh, Table of n, a(n) for n = 0..10000 FORMULA A190404: (1/2)(1 + Sum_{k>=1} (1/2)^T(k)), where T = A000217 (triangular numbers). A190405: Sum_{k>=1} (1/2)^T(k), where T = A000217 (triangular numbers). A190406: Sum_{k>=1} (1/2)^S(k-1), where S = A001844 (centered square numbers). A190407: Sum_{k>=1} (1/2)^V(k), where V = A058331 (1 + 2*k^2). EXAMPLE 0.64163256065515386629... MATHEMATICA RealDigits[EllipticTheta[2, 0, 1/Sqrt[2]]/2^(7/8) - 1, 10, 120] // First (* Jean-François Alcover, Feb 12 2013 *) RealDigits[Total[(1/2)^Accumulate[Range[50]]], 10, 120][[1]] (* Harvey P. Dale, Oct 18 2013 *) (* See also A190404 *) PROG (Sage) def A190405(b):  # Generate the constant with b bits of precision     return N(sum([(1/2)^(j*(j+1)/2) for j in range(1, b)]), b) A190405(409) # Danny Rorabaugh, Mar 25 2015 (PARI) th2(x)=2*x^.25 + 2*suminf(n=1, x^(n+1/2)^2) th2(sqrt(.5))/2^(7/8)-1 \\ Charles R Greathouse IV, Jun 06 2016 CROSSREFS Cf. A190404. Sequence in context: A021863 A259620 A299998 * A180659 A309222 A324034 Adjacent sequences:  A190402 A190403 A190404 * A190406 A190407 A190408 KEYWORD nonn,cons,easy AUTHOR Clark Kimberling, May 10 2011 STATUS approved

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Last modified October 23 04:16 EDT 2020. Contains 337962 sequences. (Running on oeis4.)