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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.
0
19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37
OFFSET
1,1
COMMENTS
The sequence has a repeating cycle of length 3.
LINKS
David G. Andersen, The Pi-Search Page.
Tom Crawford and Brady Haran, Strings and Loops within Pi, Numberphile video (2020).
FORMULA
From Stefano Spezia, Feb 22 2020: (Start)
O.g.f.: x*(19 + 37*x + 46*x^2)/(1 - x^3).
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)).
a(n) = a(n-3) for n > 3. (End)
MATHEMATICA
PadRight[{}, 100, {19, 37, 46}] (* Paolo Xausa, Apr 27 2024 *)
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Martin Renner, Feb 22 2020
STATUS
approved