A390187 - OEIS

A390187

Minimum number of distinct consecutive sums of a permutation of [n].

0, 1, 3, 5, 7, 10, 13, 17, 20, 25, 30, 33, 39, 44, 50, 56, 63, 70, 77

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OFFSET

0,3

COMMENTS

The corresponding maximum number is A389241(n).

LINKS

Table of n, a(n) for n=0..18.

Thomas Bloom, Problem 34, Erdős Problems.

Erdős problems database contributors, Issue #95 linking Erdős problems to the OEIS.

Jakub Konieczny, On consecutive sums in permutations, arXiv:1504.07156 [math.CO], 2015-2021.

EXAMPLE

For n=5, {3, 4, 1, 2, 5} is a permutation having 10 distinct consecutive sums, namely 1, 2, 3=1+2, 4, 5=4+1, 3+4=4+1+2=2+5, 3+4+1=1+2+5, 3+4+1+2, 4+1+2+5, and 3+4+1+2+5.

For n=8, {7, 6, 2, 1, 4, 3, 5, 8} and its reversal are the unique permutations that have 20 distinct consecutive sums.

MATHEMATICA

a[n_] := Min[CountDistinct[Total/@Subsequences[#, {1, \[Infinity]}]]&/@Permutations[Range[n]]]; Array[a, 6, 0]

CROSSREFS

Cf. A389241, A234813.

Sequence in context: A089108 A186355 A029899 * A072166 A077000 A195311

Adjacent sequences: A390184 A390185 A390186 * A390188 A390189 A390190

KEYWORD

nonn,hard,more

AUTHOR

Daniel Leary, Oct 28 2025

EXTENSIONS

a(16)-a(18) from Bert Dobbelaere, Nov 10 2025

STATUS

approved