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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is the first prime 2, followed by the first differences of the partition numbers of primes. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 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 Cf. A000040, A000041, A058698. Sequence in context: A133267 A145864 A306392 * A076014 A120458 A183244 Adjacent sequences:  A182736 A182737 A182738 * A182740 A182741 A182742 KEYWORD nonn AUTHOR Omar E. Pol, Jan 27 2011 EXTENSIONS More terms from Alois P. Heinz, Jan 27 2011 STATUS approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)