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 A282496 'Somos expansion' of Pi: Pi=a(0)*sqrt(a(1)*sqrt(a(2)*sqrt(a(3)*sqrt(...)))). a(n)=floor(x(n)), x(n)=x(n-1)^2/a(n-1)^2, x(0)=Pi. 1
 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 1<=a(n)<=3 for all n. Reasoning: for x>1 it follows that 1=0} a(k)^(1/2^k) = Pi. EXAMPLE Integer part of Pi is 3. Integer part of Pi^2/9 is 1. MATHEMATICA \$MaxExtraPrecision = 1000; x00 = Pi; x0 = x00; Nm = 130; j = 1; Res = Table[1, {j, 1, Nm}]; While[j < Nm, Res[[j]] = Floor[x0]; x0 = N[(x0/ Res[[j]])^2, 20000];   j++]; Res CROSSREFS Cf. A000796 (digits), A100044 (Pi^2/9), A001203 (continued fraction), A276459 (another nested radical expansion). Sequence in context: A344759 A337820 A322127 * A253238 A249773 A030369 Adjacent sequences:  A282493 A282494 A282495 * A282497 A282498 A282499 KEYWORD nonn AUTHOR Yuriy Sibirmovsky, Feb 16 2017 STATUS approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)