A182739 First differences of the partition numbers of the primes.

2, 1, 4, 8, 41, 45, 196, 193, 765, 3310, 2277, 14795, 22946, 18678, 61493, 205177, 501889, 289685, 1558184, 2017516, 1488484, 7662961, 9489819, 26657456, 83235005, 81250196, 56767824, 159900439, 110796851, 309430388, 3062487667, 2050675209, 5133105512

Offset: 1

Author

Omar E. Pol, Jan 27 2011

Keywords

• nonn

Comments

This is the first prime 2, followed by the first differences of the partition numbers of primes.

Examples

			a(5) = A000041(A000040(5)) - A000041(A000040(4)) = A000041(11) - A000041(7) = 56 - 15 = 41.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000041, A058698.

Programs

Maple

with(combinat):
a:= n-> `if`(n=1, 2, (x->x[1]-x[2])(map(numbpart@ithprime, [n, n-1]))):
seq(a(n), n=1..40);  # Alois P. Heinz, Jan 27 2011

Mathematica

Range[40] // Prime // PartitionsP // Differences // Prepend[#, 2]& (* Jean-François Alcover, Feb 21 2017 *)

Formula

a(1) = 2; a(n) = A000041(A000040(n)) - A000041(A000040(n-1)) for n>1.

Extensions

More terms from Alois P. Heinz, Jan 27 2011