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A202024
Lexicographically earliest positive integer sequence such that no sum of any number of consecutive terms is an integer of the form k^2+k+1 for any positive integer k.
0
1, 1, 4, 4, 1, 1, 4, 4, 6, 2, 2, 4, 2, 2, 2, 6, 2, 2, 2, 4, 4, 2, 2, 2, 4, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2
OFFSET
1,3
COMMENTS
After the first 16 terms, ending with ...,4,2,2,2,6, the sequence appears to consist entirely of 2's and 4's, with the spacing between successive 4's being 1,4,2,4,3,4,4,4,5,4,6,4,7,4,8,4,9,4,10,4,..., one bisection of which is 1,2,3,4,...,n,... This has been verified for the first 1000 terms.
EXAMPLE
Integers of the form k^2+k+1 for positive integer k are {3,7,13,21,...}. Assume that a(1)-a(3) have been determined as {1,1,4}. Then a(4)=1 gives consecutive terms 1,1,4,1 summing to 7, which is prohibited; a(4)=2 gives 1+4+2=7; a(4)=3 gives 4+3=7; but a(4)=4 is OK, giving no sum of consecutive terms equaling 3,7,13,... Thus a(4)=4.
CROSSREFS
Cf. A168677.
Sequence in context: A016496 A143253 A060036 * A319703 A166361 A213669
KEYWORD
nonn
AUTHOR
John W. Layman, Dec 09 2011
STATUS
approved