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A182739
First differences of the partition numbers of the primes.
1
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
1,1
COMMENTS
This is the first prime 2, followed by the first differences of the partition numbers of primes.
LINKS
FORMULA
a(1) = 2; a(n) = A000041(A000040(n)) - A000041(A000040(n-1)) for n>1.
EXAMPLE
a(5) = A000041(A000040(5)) - A000041(A000040(4)) = A000041(11) - A000041(7) = 56 - 15 = 41.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 27 2011
EXTENSIONS
More terms from Alois P. Heinz, Jan 27 2011
STATUS
approved