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 A002815 a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720. (Formerly M2523 N0996) 4
 0, 1, 3, 6, 9, 13, 17, 22, 27, 32, 37, 43, 49, 56, 63, 70, 77, 85, 93, 102, 111, 120, 129, 139, 149, 159, 169, 179, 189, 200, 211, 223, 235, 247, 259, 271, 283, 296, 309, 322, 335, 349, 363, 378, 393, 408, 423, 439, 455, 471 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) = A046992(n) + n for n > 0. [Reinhard Zumkeller, Feb 25 2012] REFERENCES H. Brocard, Reply to Query 1421, Nombres premiers dans une suite de differences, L'Intermédiaire des Mathématiciens, 7 (1900), 135-137. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 FORMULA Conjectured g.f.: (Sum_{N>=1} x^A008578(N))/(1-x)^2 = (x + x^2 + x^3 + x^5 + x^7 + x^11 + x^13 + ...)/(1-x)^2. - L. Edson Jeffery, Nov 25 2013 MATHEMATICA Table[n + Sum[PrimePi[k], {k, 1, n}], {n, 0, 50}] Module[{nn=50, pp}, pp=Accumulate[PrimePi[Range[0, nn]]]; Total/@ Thread[ {Range[ 0, nn], pp}]] (* This program is significantly faster than the program above. *) (* Harvey P. Dale, Jan 03 2013 *) PROG (Haskell) a002815 0 = 0 a002815 n = a046992 n + toInteger n  -- Reinhard Zumkeller, Feb 25 2012 CROSSREFS Cf. A000720. Sequence in context: A256966 A280944 A205726 * A109512 A025205 A024190 Adjacent sequences:  A002812 A002813 A002814 * A002816 A002817 A002818 KEYWORD nonn,nice,easy AUTHOR STATUS approved

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Last modified December 12 18:24 EST 2018. Contains 318081 sequences. (Running on oeis4.)