A294107 Maximum of the number of primes appearing among the smaller parts and the number of primes appearing among the larger parts of the partitions of n into two parts.

0, 0, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12

Offset

1,4

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for sequences related to partitions

Formula

a(n) = max(Sum_{i=1..floor(n/2)} A010051(i), Sum_{i=1..floor(n/2)} A010051(n-i)).

Mathematica

Table[Max[Sum[PrimePi[i] - PrimePi[i - 1], {i, Floor[n/2]}], Sum[PrimePi[n - i] - PrimePi[n - i - 1], {i, Floor[n/2]}]], {n, 80}]
mnp[n_]:=Module[{ps=IntegerPartitions[n, {2}]}, Max[Count[ ps[[All, 1]], _?PrimeQ], Count[ ps[[All, 2]], _?PrimeQ]]]; Array[mnp, 80] (* Harvey P. Dale, Sep 12 2021 *)

Crossrefs

Cf. A010051, A294108.

Sequence in context: A240708 A235645 A325357 * A240874 A029379 A058776

Adjacent sequences: A294104 A294105 A294106 * A294108 A294109 A294110

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved