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SmallestMissingPart on IntegerPartition ​

The smallest positive integer that is not a part.

On IntegerPartition

Called as CombinatorialStat(x, "SmallestMissingPart"). The head's page has its examples.

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FindStat St000759

The smallest missing part in an integer partition.

ObjectValue
[]1
[1]2
[2]1
[3]1
[4]1
[5]1
[6]1
[7]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000759 has the rest.