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A060620
Average of the first n primes rounded down.
10
2, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 33, 35, 38, 40, 42, 44, 46, 48, 51, 53, 55, 57, 60, 62, 65, 67, 69, 72, 74, 77, 79, 82, 84, 87, 89, 91, 94, 97, 99, 102, 104, 107, 110, 112, 115, 117, 120, 123, 125, 128, 130, 133, 136, 138, 141, 144
OFFSET
1,1
COMMENTS
Closely related to the prime number theorem; a(n) has the asymptotic expression n * log(n) / 2.
FORMULA
a(n) = floor(A007504(n) / n).
EXAMPLE
a(5) = floor((2 + 3 + 5 + 7 + 11)/5) = 5.
MATHEMATICA
With[{prms=Prime[Range[500]]}, Table[Floor[Mean[Take[prms, n]]], {n, 70}]] (* Harvey P. Dale, Mar 09 2011 *)
PROG
(PARI) { n=0; s=0; forprime (p=2, prime(1000), s+=p; write("b060620.txt", n++, " ", floor(s/n)); ) } \\ Harry J. Smith, Jul 08 2009
(PARI) a(n) = sum(k=1, n, prime(k))\n; \\ Michel Marcus, Jul 03 2018
CROSSREFS
Sequence in context: A125573 A034139 A238886 * A109968 A011872 A056822
KEYWORD
nonn,easy
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 25 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2001
STATUS
approved