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 A257574 Continued square root map applied to the sequence of positive even numbers, (2, 4, 6, 8, ...). 22
 2, 1, 5, 8, 4, 7, 6, 8, 7, 2, 3, 1, 1, 0, 3, 9, 7, 6, 5, 6, 5, 5, 8, 5, 3, 4, 7, 9, 8, 0, 7, 0, 2, 5, 2, 4, 1, 6, 6, 9, 6, 9, 4, 4, 4, 0, 3, 5, 4, 2, 8, 6, 6, 7, 0, 3, 7, 5, 5, 0, 9, 6, 3, 4, 2, 1, 9, 4, 6, 2, 4, 0, 7, 4, 5, 4, 9, 7, 7, 1, 1, 8, 5, 9, 9, 8, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The continued square root or CSR map applied to a sequence b = (b(1), b(2), b(3), ...) is the number CSR(b) := sqrt(b(1)+sqrt(b(2)+sqrt(b(3)+sqrt(b(4)+...)))). Taking out a factor sqrt(2), one gets CSR(2, 4, 6, 8, ...) = sqrt(2) CSR(1, 1, 3/8, 1/32, ...) < A002193*A001622 = (sqrt(5)+1)/sqrt(2). - M. F. Hasler, May 01 2018 LINKS Hiroaki Yamanouchi, Table of n, a(n) for n = 1..400 A. Herschfeld, On Infinite Radicals, Amer. Math. Monthly, 42 (1935), 419-429. Herman P. Robinson, The CSR Function, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy. EXAMPLE sqrt(2 + sqrt(4 + sqrt(6 + sqrt(8 + ...)))) = 2.1584768723110397656558534... PROG (PARI) (CSR(v, s)=forstep(i=#v, 1, -1, s=sqrt(v[i]+s)); s); t=0; for(N=5, oo, (t==t=Str(CSR([1..2*N]*2)))&&break; print(2*N": "t)) \\ Allows to see the convergence, which is reached when length of vector ~ precision [given as number of digits]. Using Str() to avoid infinite loop when internal representation is "fluctuating". - M. F. Hasler, May 04 2018 CROSSREFS Cf. A072449, A257575..A257581, A105817, A099879, A001622, A105546. Sequence in context: A108599 A108590 A109233 * A316293 A193180 A201743 Adjacent sequences:  A257571 A257572 A257573 * A257575 A257576 A257577 KEYWORD nonn,cons AUTHOR N. J. A. Sloane, May 02 2015 EXTENSIONS a(27)-a(87) from Hiroaki Yamanouchi, May 03 2015 Edited by M. F. Hasler, May 01 2018 STATUS approved

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Last modified June 6 04:15 EDT 2020. Contains 334859 sequences. (Running on oeis4.)