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A332756 A loop sequence within Pi. Let a(1) = 19. For n > 1, a(n+1) is the position of the first occurrence of a(n) after the decimal point in the decimal expansion of Pi.

%I A332756 #13 Apr 28 2024 09:51:27
%S A332756 19,37,46,19,37,46,19,37,46,19,37,46,19,37,46,19,37,46,19,37,46,19,37,
%T A332756 46,19,37,46,19,37,46,19,37,46,19,37,46,19,37,46,19,37,46,19,37,46,19,
%U A332756 37,46,19,37,46,19,37,46,19,37,46,19,37,46,19,37,46,19,37
%N A332756 A loop sequence within Pi. Let a(1) = 19. For n > 1, a(n+1) is the position of the first occurrence of a(n) after the decimal point in the decimal expansion of Pi.
%C A332756 The sequence has a repeating cycle of length 3.
%H A332756 David G. Andersen, <a href="https://www.angio.net/pi/piquery">The Pi-Search Page</a>.
%H A332756 Tom Crawford and Brady Haran, <a href="https://www.youtube.com/watch?v=W20aT14t8Pw">Strings and Loops within Pi</a>, Numberphile video (2020).
%H A332756 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A332756 From _Stefano Spezia_, Feb 22 2020: (Start)
%F A332756 O.g.f.: x*(19 + 37*x + 46*x^2)/(1 - x^3).
%F A332756 E.g.f.: 34*(cosh(x) + sinh(x)) - 46 - 6*exp(-x/2)*(sqrt(3)*sin(sqrt(3)*x/2) - 2*cos(sqrt(3)*x/2)).
%F A332756 a(n) = a(n-3) for n > 3. (End)
%t A332756 PadRight[{}, 100, {19, 37, 46}] (* _Paolo Xausa_, Apr 27 2024 *)
%Y A332756 Cf. A000796, A057680, A097614, A247345.
%K A332756 easy,nonn,base
%O A332756 1,1
%A A332756 _Martin Renner_, Feb 22 2020