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A007759 Knopfmacher expansion of sqrt(2): a(2n)=2(a(2n-1)+1)^2 - 1, a(2n+1)=2a(2n)^2 - 2. 0

%I

%S 2,17,576,665857,886731088896,1572584048032918633353217,

%T 4946041176255201878775086487573351061418968498176,

%U 48926646634423881954586808839856694558492182258668537145547700898547222910968507268117381704646657

%N Knopfmacher expansion of sqrt(2): a(2n)=2(a(2n-1)+1)^2 - 1, a(2n+1)=2a(2n)^2 - 2.

%H A. Knopfmacher and J. Knopfmacher, <a href="https://doi.org/10.1007/978-94-009-1910-5_24">An alternating product representation for real numbers</a>, in Applications of Fibonacci numbers, Vol. 3 (Kluwer 1990), pp. 209-216.

%o (PARI) a(n) = if (n==1, 2, if (n % 2, 2*a(n-1)^2 - 2, 2*(a(n-1)+1)^2 - 1)); \\ _Michel Marcus_, Feb 20 2019

%Y Cf. A002193 (sqrt(2)), A001601.

%K nonn

%O 1,1

%A _Arnold Knopfmacher_

%E More terms from _Christian G. Bower_, Jan 06 2006

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Last modified July 17 23:21 EDT 2019. Contains 325109 sequences. (Running on oeis4.)