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A168677 Lexicographically earliest positive integer sequence such that no sum of consecutive terms is a positive power of 4. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..105.

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

FORMULA

a(n)=(1/56)*{-51*(n mod 8)+5*[(n+1) mod 8]+5*[(n+2) mod 8]+33*[(n+3) mod 8]-23*[(n+4) mod 8]+5*[(n+5) mod 8]+5*[(n+6) mod 8]+61*[(n+7) mod 8]}, with n>=1 [From Paolo P. Lava, Dec 14 2009]

EXAMPLE

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,... .

MATHEMATICA

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

CROSSREFS

Sequence in context: A066504 A292771 A322837 * A140210 A010130 A206773

Adjacent sequences:  A168674 A168675 A168676 * A168678 A168679 A168680

KEYWORD

nonn

AUTHOR

John W. Layman, Dec 02 2009

STATUS

approved

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Last modified April 18 16:56 EDT 2019. Contains 322229 sequences. (Running on oeis4.)