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A318709
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Decimal expansion of the solution to x = sqrt(5 + sqrt(5 - sqrt(5 - sqrt(5 + x)))).
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1
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2, 6, 2, 1, 4, 0, 8, 3, 8, 3, 0, 7, 5, 8, 6, 1, 5, 0, 5, 6, 9, 8, 4, 9, 5, 2, 8, 0, 6, 1, 2, 2, 4, 3, 1, 2, 7, 7, 9, 7, 9, 7, 0, 6, 1, 4, 7, 2, 1, 1, 6, 7, 6, 7, 9, 6, 6, 4, 1, 6, 7, 8, 2, 5, 3, 9, 3, 9, 6, 3, 1, 3, 6, 7, 6, 5, 7, 9
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OFFSET
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1,1
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COMMENTS
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The last part of Ramanujan's question 722 in the Journal of the Indian Mathematical Society (VII, 240) asked "... deduce that, if x = sqrt(5 + sqrt(5 - sqrt(5 - sqrt(5 + x)))), then x = (1/4) * (sqrt(5) - 2 + sqrt(13 - 4 * sqrt(5)) + sqrt(50 + 12 * sqrt(5) - 2 * sqrt(65 - 20 * sqrt(5))))".
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LINKS
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EXAMPLE
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2.6214083830758615056984952806122431277979706147211676796641678...
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PROG
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(PARI) solve(x=2, 3, x-sqrt(5+sqrt(5-sqrt(5-sqrt(5+x)))))
(PARI) (1/4)*(sqrt(5)-2+sqrt(13-4*sqrt(5))+sqrt(50+12*sqrt(5)-2*sqrt(65-20*sqrt(5))))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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