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1

1 1

2 0 1

3 1 0 1

4 2 0 0 1

6 3 1 0 0 1

8 4 2 0 0 0 1

11 6 3 1 0 0 0 1

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Median of prime indices is A360005(n)/2.

The A high version for mean instead of above median is A363946, rank statistic stat A363944.

A067538 counts partitions with integer mean, ranked by A316413.

A362608 counts partitions with a unique mode, ranks A356862.

A363486 gives low mode A360005(n)/2 returns median of prime indices, high A363487.

Cf. A025065, A026794, A027193, A067538, A237984, A240219, `A363726, `A362608, A363740.

Cf. A124944, A026794, A008284, A000041 (row sums), A027336 (1st column).

Row sums are A000041.

A000041 counts integer partitions, strict A000009.

Cf. A025065, A026794, A027193, A237984, A240219, `A363726, `A363740.

From Gus Wiseman, Jul 09 2023: (Start)

Row n = 8 counts the following partitions:

(71) (62) (53) (44) . . . (8)

(611) (521) (431)

(5111) (422) (332)

(4211) (3221)

(41111) (2222)

(3311) (22211)

(32111)

(311111)

(221111)

(2111111)

(11111111)

(End)

Column k = 1 is A027336, ranks A363488.

The high version of this triangle is A124944.

Median of prime indices is A360005(n)/2.

The rank statistic for this triangle is A363941, high version A363942.

A version for mean instead of median is A363945, rank statistic A363943.

The high version of above is A363946, rank statistic A363944.

A version for mode instead of median is A363952, high A363953.

A000041 counts integer partitions, strict A000009.

A008284 counts partitions by length (or decreasing mean), strict A008289.

A067538 counts partitions with integer mean, ranked by A316413.

A325347 counts partitions with integer median, ranks A359908.

A359893 and A359901 count partitions by median.

A362608 counts partitions with a unique mode, ranks A356862.

A363486 gives low mode of prime indices, high A363487.

Cf. A025065, A027193, A237984, A240219, `A363726, `A363740.

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Arrange the parts of a partition non-increasing nonincreasing order. Remove the first part, then the last, then the first remaining part, then the last remaining part, and continue until only a single number, the low median, remains. - Clark Kimberling, May 16 2019

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