OFFSET
0,3
REFERENCES
H. Brocard, Reply to Query 1421, Nombres premiers dans une suite de différences, 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
(Python)
from sympy import primerange
def A002815(n): return n+(n+1)*len(p:=list(primerange(n+1)))-sum(p) # Chai Wah Wu, Jan 01 2024
(PARI) a(n) = my(p=primes([0, n])); n + (n+1)*#p - vecsum(p); \\ Ruud H.G. van Tol, Feb 16 2024
CROSSREFS
KEYWORD
nonn,nice,easy
STATUS
approved