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For n<=11, a(n) = n mod 10. For even n>11, a(n) = (2a(n-1)+1) mod 10. For odd n>11, a(n) = (a(n-1)+a(i+1)) mod 10, where i is the largest integer < n-1 such that a(i)=a(n-1).
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%I #8 Feb 12 2024 12:09:09

%S 0,1,2,3,4,5,6,7,8,9,0,1,3,7,5,1,3,0,1,4,9,9,9,8,7,2,5,6,3,3,7,9,9,8,

%T 7,6,3,0,1,5,1,6,3,3,7,3,7,0,1,7,5,6,3,0,1,8,7,2,5,1,3,3,7,9,9,8,7,6,

%U 3,0,1,4,9,7,5,6,3,3,7,2,5,1,3,0,1,4,9,6,3,3,7,9,9,8,7,6,3,0,1,5,1,6,3,3,7

%N For n<=11, a(n) = n mod 10. For even n>11, a(n) = (2a(n-1)+1) mod 10. For odd n>11, a(n) = (a(n-1)+a(i+1)) mod 10, where i is the largest integer < n-1 such that a(i)=a(n-1).

%C The sequence has period 60 starting with a(27).

%H Ray Chandler, <a href="/A081286/b081286.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_60">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%Y Cf. A080867.

%K nonn,easy

%O 0,3

%A _Dean Hickerson_, based on information supplied by Laurent Dorey and Antti Karttunen, Mar 15 2003.