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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)