

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
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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.


LINKS

Table of n, a(n) for n=1..87.


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
Adjacent sequences: A202021 A202022 A202023 * A202025 A202026 A202027


KEYWORD

nonn


AUTHOR

John W. Layman, Dec 09 2011


STATUS

approved



