A002815 a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720. (Formerly M2523 N0996)

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

Offset

0,3

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

a(n) = A046992(n) + n for n > 0. - Reinhard Zumkeller, Feb 25 2012

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: A280944 A330321 A205726 * A342711 A109512 A025205

Adjacent sequences: A002812 A002813 A002814 * A002816 A002817 A002818

Keyword

nonn,nice,easy,changed

Author

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Status

approved