login
A086609
Number of primes between consecutive partition numbers.
1
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 11 2003
EXTENSIONS
Terms a(42) and beyond from Andrew Howroyd, Jan 05 2020
STATUS
approved