STATUS
reviewed
approved
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Revision History for A215608
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
proposed
reviewed
STATUS
editing
proposed
NAME
Decimal expansion of the "value" -sum(Sum_{n>=1, } (-1)^n / n^(1/n) ).
CROSSREFS
Cf. A073009.
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
MATHEMATICA
digits = 69; a[n_] := 1/n^(1/n); a[0] = 0; Clear[f]; f[n_] := f[n] = (d = (3+Sqrt[8])^n; d = (d+1/d)/2; b = 1; c = d; s = 0; For[k = 0, k <= n-1, k++, c = b-c; s = s+c*a[k]; b = (k+n)*(k-n)*b / ((k+1/2)*(k+1))]; s/d) // RealDigits[#, 10, digits] & // First; f[0] ; f[n = 10] ; While[f[n] != f[n-10], n = n+10]; f[n] (* Jean-François Alcover, Mar 06 2013 *)
MATHEMATICA
digits = 69; a[n_] := 1/n^(1/n); a[0] = 0; Clear[f]; f[n_] := f[n] = (d = (3+Sqrt[8])^n; d = (d+1/d)/2; b = 1; c = d; s = 0; For[k = 0, k <= n-1, k++, c = b-c; s = s+c*a[k]; b = (k+n)*(k-n)*b / ((k+1/2)*(k+1))]; s/d) // RealDigits[#, 10, digits] & // First; f[0] ; f[n = 10] ; While[ f[n] != f[n-10], n = n+10]; f[n] (* Jean-François Alcover, Mar 06 2013 *)
STATUS
approved
editing
STATUS
editing
approved
DATA
0, 6, 3, 7, 0, 9, 2, 0, 8, 5, 8, 9, 8, 4, 9, 4, 7, 4, 7, 9, 1, 1, 2, 5, 5, 6, 0, 8, 1, 7, 1, 2, 8, 4, 5, 1, 5, 5, 4, 4, 0, 1, 8, 3, 1, 4, 0, 1, 5, 9, 6, 0, 4, 6, 7, 2, 3, 8, 7, 8, 0, 0, 0, 6, 5, 8, 2, 2, 1, 5
OFFSET
0,21
STATUS
approved
editing