A168677 Lexicographically earliest positive integer sequence such that no sum of consecutive terms is a positive power of 4.

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, 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, 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

Offset: 1

Author

John W. Layman, Dec 02 2009

Keywords

• nonn

Comments

It appears that the sequence is periodic with period (1,1,1,5,1,1,1,9) of length 8.

Examples

			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,... .
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Programs

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1},{1, 1, 1, 5, 1, 1, 1, 9},105] (* Ray Chandler, Aug 25 2015 *)