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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

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

STATUS

approved

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Last modified December 13 19:20 EST 2017. Contains 295976 sequences.