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%I #12 Sep 25 2012 06:30:44
%S 1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,3,1,
%T 1,1,1,1,1,1,1,3,1,1,9,4,4,3,1,4,3,1,1,9,4,4,3,1,1,3,1,1,1,1,1,1,2,1,
%U 1,1,1,1,1,1,1,1,4,3,1,1,1,1,3,1,1,4,3
%N First occurrence of an 'average' valued sequence of length 2n in the Kolakoski sequence (A000002).
%C a(n) is the least k such that K(k) + K(k+1) + ... + K(k + 2*n - 1) = 3*n, where K(m) = A000002(m).
%H Nathaniel Johnston, <a href="/A074298/b074298.txt">Table of n, a(n) for n = 1..10000</a>
%e a[1]=1, as A000002 begins 1,2 (sum 3) a[2]=1, as A000002 begins 1,2,2,1 (sum 6) a[3]=1, as A000002 begins 1,2,2,1,1,2 (sum 9).
%t nmax = 90; a2 = {1, 2, 2}; For[n = 3, n <= 2*nmax, n++, For[i = 1, i <= a2[[n]], i++, AppendTo[a2, 1 + Mod[n - 1, 2]]]]; a[n_] := For[k = 1, True, k++, If[Plus @@ a2[[k ;; k + 2*n - 1]] == 3*n, Return[k]]]; Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, Sep 25 2012 *)
%Y Cf. A074296, A074297, A074299.
%K nonn
%O 1,6
%A _Jon Perry_, Sep 21 2002
%E Offset corrected by _Nathaniel Johnston_, May 02 2011
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