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A301514
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Infinite nested radical negated: i*sqrt(1+2i*sqrt(1+3i*sqrt(1+4i*sqrt(1+5i*sqrt(1+...))))).
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1
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2, 4, 9, 4, 6, 2, 5, 1, 4, 7, 5, 4, 1, 0, 0, 9, 2, 9, 0, 1, 8, 7, 2, 2, 7, 1, 3, 0, 0, 0, 4, 0, 7, 7, 4, 5, 1, 2, 6, 8, 7, 7, 3, 3, 6, 6, 7, 0, 8, 4, 1, 3, 9, 6, 1, 4, 7, 5, 5, 9, 2, 3, 0, 0, 4, 4, 3, 4, 3, 3, 9, 6, 4, 9, 9, 1, 2, 2, 0, 9, 9, 2, 5, 3, 2, 8, 2, 9, 3, 2, 1, 4, 9, 6, 5, 0, 9, 7, 8, 9, 3, 0, 1, 2, 6
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OFFSET
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1,1
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COMMENTS
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Inspired by Ramanujan's infinite nested radical of natural numbers.
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REFERENCES
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Ramanujan's 2nd Notebook, Chapter XII, Page 108, entry 4.
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LINKS
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EXAMPLE
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2.4946251475410092901872271300040774512687733667084139614755923004434339649...
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MATHEMATICA
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RealDigits[Chop[N[-I*Fold[#2*Sqrt[1 + #1*I] &, 0, Reverse[Range[400]]], 125]], 10, 120][[1]] (* Vaclav Kotesovec, Dec 22 2018 *)
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PROG
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(PARI)
b(n) = imag(fold((x, y)->sqrt(1+x*y), Vecrev([2..n+1])*I));
N=106; default(realprecision, N); limitnum(b, , 4) \\ Gheorghe Coserea, Dec 23 2018
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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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