A301514 Infinite nested radical negated: i*sqrt(1+2i*sqrt(1+3i*sqrt(1+4i*sqrt(1+5i*sqrt(1+...))))).

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

Offset

1,1

Comments

Inspired by Ramanujan's infinite nested radical of natural numbers.

References

Ramanujan's 2nd Notebook, Chapter XII, Page 108, entry 4.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10001

Example

2.4946251475410092901872271300040774512687733667084139614755923004434339649...

Mathematica

RealDigits[Chop[N[-I*Fold[#2*Sqrt[1 + #1*I] &, 0, Reverse[Range[400]]], 125]], 10, 120][[1]] (* Vaclav Kotesovec, Dec 22 2018 *)

Prog

(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

Crossrefs

Cf. A072449, A239349.

Sequence in context: A021405 A201946 A341352 * A269063 A161360 A230242

Adjacent sequences: A301511 A301512 A301513 * A301515 A301516 A301517

Keyword

cons,nonn

Author

Robert G. Wilson v, Dec 15 2018

Status

approved