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A239349
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Decimal expansion of prime version of Ramanujan's infinite nested radical.
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19
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9, 4, 0, 5, 0, 4, 3, 6, 1, 2, 4, 4, 5, 2, 1, 7, 5, 7, 8, 1, 3, 7, 6, 3, 3, 7, 4, 2, 9, 7, 8, 6, 0, 0, 5, 7, 9, 4, 1, 8, 7, 5, 6, 5, 2, 2, 5, 9, 0, 2, 3, 6, 3, 9, 6, 5, 9, 2, 2, 1, 7, 2, 1, 8, 5, 6, 0, 6, 8, 5, 9, 4, 2, 4, 2, 2, 1, 9, 9, 1, 2, 9, 8, 7, 3, 7, 7, 4, 0, 1, 4, 1, 0, 4, 9, 2, 9, 0, 6, 2, 8, 5, 5, 8, 9, 1, 8, 2, 6, 9
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OFFSET
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1,1
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COMMENTS
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Replace each factor n = 1, 2, 3, ... with prime(n) = 2, 3, 5, ... in Ramanujan's infinite nested radical 1*sqrt(1 + 2*sqrt(1 + 3*sqrt(1 + ...))) = 3, obtaining 2*sqrt(1 + 3*sqrt(1 + 5*sqrt(1 + ...))) = 9.405043....
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REFERENCES
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S. Ramanujan, J. Indian Math. Soc., III (1911), 90 and IV (1912), 226.
T. Vijayaraghavan, in Collected Papers of Srinivasa Ramanujan, G. H. Hardy, P. V. Seshu Aiyar and B. M. Wilson, eds., Cambridge Univ. Press, 1927, p. 348; reprinted by Chelsea, 1962.
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LINKS
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FORMULA
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Equals 2*sqrt(1 + 3*sqrt(1 + 5*sqrt(1 + 7*sqrt(1 + 11*sqrt(1 + ...))))).
Lim_{n->infinity} 2*sqrt(1 + 3*sqrt(1 + 5*sqrt(1 + ... + prime(n)*sqrt(1))))).
sqrt(4 + sqrt(144 + sqrt(129600 + ...))) = sqrt(A(1) + sqrt(A(2) + sqrt(A(3) + ...))), where A = A239350 = superprimorials squared.
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EXAMPLE
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9.4050436124452175781376337429786005794187565225902363965922...
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MATHEMATICA
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RealDigits[ Fold[ #2*Sqrt[ 1 + #1] &, 0, Reverse[ Prime[ Range[ 400]]]], 10, 110][[1]]
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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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