A382749 Position in block for greedy partition of length 4.

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

Offset: 1

Author

Jan Snellman, Apr 24 2025

Keywords

• nonn

Comments

a(n) = height of n with respect to the greedy convolution of length 4.

Position of n i block containing it for the greedy partition of length 4 of the positive integers.

a(n) = the column (one-indexed) in which n occurs in the infinite matrix A382747.

Links

• Jan Snellman, Table of n, a(n) for n = 1..5000
• W. Narkiewicz, On a class of arithmetical convolutions, Colloq. Math. 10, 1963, pp 81--94.
• Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Crossrefs

a(n) = column index of the unique position in the infinite matrix A382747 in which n occurs.

a(n) = 1 iff n is "primitive" with respect to the greedy convolution of length 4 i.e. if n occurs in A382748.