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A120703
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Decimal expansion of limiting difference of n - Sum[Cos[Pi/2^k],{k,0,n}].
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1
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2, 3, 9, 4, 6, 4, 9, 8, 0, 2, 1, 2, 5, 1, 6, 5, 5, 5, 9, 2, 2, 1, 0, 0, 3, 1, 4, 2, 7, 1, 2, 0, 7, 3, 0, 9, 3, 9, 1, 1, 5, 4, 7, 1, 9, 2, 5, 6, 1, 2, 3, 0, 4, 1, 2, 3, 0, 8, 3, 0, 9, 3, 8, 4, 5, 8, 3, 3, 3, 3, 8, 1, 5, 8, 8, 5, 8, 9, 1, 9
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Limit[n - Sum[Cos[Pi/2^k],{k,0,n}], n -> Infinity] Integrate[Sum[2^(-m)*(Sin[2^m*x] + Sin[2^-m*x]), {m, 0, 40}], {x, 0, 2*Pi}] - 1
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EXAMPLE
| 2.3946498021251655592210031427120730939115471925612304123083093845833338...
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MATHEMATICA
| N[n - Sum[Cos[Pi/2^k], {k, 0, n}] /. n -> 300, 80] RealDigits[%, 10]
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CROSSREFS
| Decimal expansion of corresponding limiting ratio given by A120704.
Sequence in context: A093319 A160388 A026195 * A089206 A202017 A127198
Adjacent sequences: A120700 A120701 A120702 * A120704 A120705 A120706
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KEYWORD
| cons,nonn
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AUTHOR
| Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 28 2006
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