A086609 Number of primes between consecutive partition numbers.

0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 6, 8, 10, 12, 14, 17, 21, 24, 30, 36, 44, 49, 63, 71, 87, 100, 120, 143, 164, 200, 226, 272, 318, 368, 432, 499, 593, 681, 792, 912, 1069, 1228, 1437, 1641, 1900, 2177, 2530, 2896, 3348, 3832, 4379, 5039, 5775, 6582, 7516

Offset

0,8

Links

Andrew Howroyd, Table of n, a(n) for n = 0..150

Formula

a(n) = A000720(A000041(n+1)) - A000720(A000041(n)).

Mathematica

PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[PartitionsP[Range[0, 100]], 2, 1] (* Harvey P. Dale, Sep 13 2021 *)

Prog

(PARI) a(n)={primepi(numbpart(n+1)) - primepi(numbpart(n))} \\ Andrew Howroyd, Jan 05 2020

Crossrefs

Cf. A000040, A000041, A000720.

Sequence in context: A325391 A179254 A304430 * A341140 A340285 A341462

Adjacent sequences: A086606 A086607 A086608 * A086610 A086611 A086612

Keyword

nonn

Author

Reinhard Zumkeller, Sep 11 2003

Extensions

Terms a(42) and beyond from Andrew Howroyd, Jan 05 2020

Status

approved