A168677 -id:A168677 - cp's OEIS frontend

A171465 Lexicographically earliest positive integer sequence such that no sum of consecutive terms is a positive square.

2, 3, 2, 3, 2, 3, 2, 3, 2, 12, 5, 5, 8, 5, 5, 3, 2, 5, 13, 10, 14, 10, 5, 3, 3, 2, 5, 5, 5, 3, 20, 7, 3, 2, 5, 5, 5, 7, 6, 5, 23, 5, 6, 6, 2, 3, 2, 5, 5, 3, 37, 5, 5, 5, 5, 3, 5, 5, 5, 19, 8, 13, 2, 5, 28, 5, 7, 5, 5, 2, 15, 38, 5, 3, 2, 3, 2, 3, 2, 32, 18, 17, 6, 5, 13, 6, 33, 11, 2, 15, 22, 2, 3, 17

Offset: 1

John W. Layman, Dec 09 2009

nonn

Let T(a) be the sequence of all positive integers (in order of increasing magnitude) that are not a sum of any number of consecutive terms of a, and let s be the sequence of positive squares. An interesting question is whether T(a) = s. Calculation shows that if 100 terms of a are used then T(a) agrees with s for the first 13 terms; if 1000 terms of a are used then T(a) agrees with s for the first 57 terms.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A171465

Cf. A168677, A332941 (prime variant).

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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.

Original entry on oeis.org

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

John W. Layman, Dec 09 2011

nonn

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.

			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.

Cf. A168677.

cp's OEIS Frontend

A171465 Lexicographically earliest positive integer sequence such that no sum of consecutive terms is a positive square.

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