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Denominators in an expansion for sqrt(2).
0

%I #17 Aug 03 2013 06:42:09

%S 2,11,780,180120,602397129892,1056102638179040007288663,

%T 327737656399044928534482808981921590582331458173

%N Denominators in an expansion for sqrt(2).

%C Denominators of an alternating series for sqrt(2) where the n-th numerator is the n-th digit of Pi, see example. - _Michel Marcus_, Aug 03 2013

%e Sqrt(2) = 3/2 + (-1)/11 + 4/780 + (-1)/180120 + 5/602397129892 + (-9)/1056102638179040007288663 + ... with successive digits of Pi as numerators.

%o (PARI) a(nn) = {vpi = digits(floor(Pi*10^(nn-1)), 10); val = 0; isign = 1; for (i=1, #vpi, ai = floor((isign*vpi[i])/(sqrt(2)-val)); print1(ai, ", "); val += isign * vpi[i]/ai; isign *= -1;);} \\ _Michel Marcus_, Aug 01 2013

%Y Cf. A002193.

%K nonn,base

%O 1,1

%A _Yalcin Aktar_, Apr 12 2004, Feb 22 2007