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

Author

John W. Layman, Dec 09 2009

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

Cf. A168677, A332941 (prime variant).

Programs

PARI

See Links section.