The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A239349 Decimal expansion of prime version of Ramanujan's infinite nested radical. 15
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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.... Converges by Vijayaraghavan's test or Herschfeld's test, together with the Prime Number Theorem. - Petros Hadjicostas and Jonathan Sondow, Mar 23 2014 REFERENCES 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. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 A. Herschfeld, On Infinite Radicals, Amer. Math. Monthly, 42 (1935), 419-429. Jonathan Sondow and Petros Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl., 332 (2007), 292-314; see pp. 305-306. Wikipedia, Tirukkannapuram Vijayaraghavan. FORMULA 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. EXAMPLE 9.4050436124452175781376337429786005794187565225902363965922... MATHEMATICA RealDigits[ Fold[ #2*Sqrt[ 1 + #1] &, 0, Reverse[ Prime[ Range[ 400]]]], 10, 110][[1]] CROSSREFS Cf. A105546, A239350. Sequence in context: A116393 A198111 A194562 * A198675 A203131 A259484 Adjacent sequences:  A239346 A239347 A239348 * A239350 A239351 A239352 KEYWORD cons,nonn AUTHOR Jonathan Sondow, Mar 16 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 03:13 EDT 2020. Contains 337266 sequences. (Running on oeis4.)