A381597 Lexicographically earliest sequence of positive integers such that for any t and k, with k>=1, where t = a(n) = a(n+k) = a(n+2*k), only one occurrence of k, for a given t, appears anywhere in the sequence.

1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 3, 2, 3, 2, 1, 3, 1, 2, 3, 2, 2, 1, 3, 3, 2, 1, 2, 3, 3, 3, 1, 1, 4, 1, 2, 3, 4, 3, 1, 3, 1, 4, 4, 2, 3, 2, 2, 4, 3, 4, 2, 4, 4, 2, 1, 4, 1, 3, 2, 2, 4, 5, 3, 1, 3, 3, 1, 4, 4, 2, 4, 4, 3, 1, 1, 2, 3, 3, 2, 5, 5, 3, 5, 2, 1, 3, 4, 5, 4, 1, 5, 4, 3, 1, 2, 4, 1, 4, 1, 5, 2, 2, 3, 3, 5, 5, 5, 4, 5, 1, 4, 3, 2, 5

Offset

1,4

Comments

See A381599 for the index where n first appears, and A381598 for the index where three consecutive n's appears.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Example

a(1) = a(2) = a(3) = 1, which is the first appearance of three 1's separated by one term.
a(4) = 2 as 1 cannot be chosen as that would form a(2) = a(3) = a(4) = 1, but three 1's separated by one term has already appeared.
a(5) = 1, which also forms three 1's separated by two terms, a(1) = a(3) = a(5) = 1.
a(17) = 3 as 1 cannot be chosen as that would form a(15) = a(16) = a(17) = 1, but three 1's separated by one term has already appeared, while choosing 2 would form a(11) = a(14) = a(17) = 2, but three 2's separated by three terms has already appeared at a(4) = a(7) = a(10) = 2.

Crossrefs

Cf. A381598 (triplets), A381599 (where n first appears), A370708 (indices where 1's appear), A281511, A229037.

Sequence in context: A141272 A380560 A281527 * A124038 A378398 A029311

Adjacent sequences: A381594 A381595 A381596 * A381598 A381599 A381600

Keyword

nonn,new

Author

Scott R. Shannon, Mar 01 2025

Status

approved