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%I #8 Sep 13 2021 18:33:25
%S 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,
%T 100,120,143,164,200,226,272,318,368,432,499,593,681,792,912,1069,
%U 1228,1437,1641,1900,2177,2530,2896,3348,3832,4379,5039,5775,6582,7516
%N Number of primes between consecutive partition numbers.
%H Andrew Howroyd, <a href="/A086609/b086609.txt">Table of n, a(n) for n = 0..150</a>
%F a(n) = A000720(A000041(n+1)) - A000720(A000041(n)).
%t PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[PartitionsP[Range[0,100]],2,1] (* _Harvey P. Dale_, Sep 13 2021 *)
%o (PARI) a(n)={primepi(numbpart(n+1)) - primepi(numbpart(n))} \\ _Andrew Howroyd_, Jan 05 2020
%Y Cf. A000040, A000041, A000720.
%K nonn
%O 0,8
%A _Reinhard Zumkeller_, Sep 11 2003
%E Terms a(42) and beyond from _Andrew Howroyd_, Jan 05 2020
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