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%I #11 Dec 14 2023 05:20:22
%S 1,1,1,5,1,1,1,9,1,1,1,5,1,1,1,9,1,1,1,5,1,1,1,9,1,1,1,5,1,1,1,9,1,1,
%T 1,5,1,1,1,9,1,1,1,5,1,1,1,9,1,1,1,5,1,1,1,9,1,1,1,5,1,1,1,9,1,1,1,5,
%U 1,1,1,9,1,1,1,5,1,1,1,9,1,1,1,5,1,1,1,9,1,1,1,5,1,1,1,9,1,1,1,5,1,1,1,9,1
%N Lexicographically earliest positive integer sequence such that no sum of consecutive terms is a positive power of 4.
%C It appears that the sequence is periodic with period (1,1,1,5,1,1,1,9) of length 8.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).
%e Assume that a(1) - a(7) have been determined as {1,1,1,5,1,1,1}. Then a(8)=1 gives consecutive terms 1,1,1,1, summing to 4; a(8)=2 gives 1+1+2=4; ... etc...; a(8)=8 gives 5+1+1+1+8=16; but a(8)=9 is ok, giving no sum of consecutive terms equalling 4,16,64,... .
%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1},{1, 1, 1, 5, 1, 1, 1, 9},105] (* _Ray Chandler_, Aug 25 2015 *)
%K nonn
%O 1,4
%A _John W. Layman_, Dec 02 2009
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