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A102781 Number of even numbers less than the n-th prime. 11
0, 1, 2, 3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, 23, 26, 29, 30, 33, 35, 36, 39, 41, 44, 48, 50, 51, 53, 54, 56, 63, 65, 68, 69, 74, 75, 78, 81, 83, 86, 89, 90, 95, 96, 98, 99, 105, 111, 113, 114, 116, 119, 120, 125, 128, 131, 134, 135, 138, 140, 141, 146, 153, 155, 156 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Same as A005097 ((odd primes - 1)/2) with a leading zero. (Lambert Klasen, Nov 06 2005)

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000

FORMULA

Integer part of p#/((p-2)#*2#), where p=prime(n) and i# is the primorial function A034386(i). - Cino Hilliard, Feb 25 2005

a(n) = prime_n - floor((prime_n)/2) - 1. Giovanni Teofilatto, Nov 05 2005

n# = product of primes <= n. 0#=1#=2. n#/(n-r)#/r# is analogous to the number of combinations of n things taken r at a time: C(n, r) = n!/ (n-r)!/r! where factorial ! is replaced by primorial #.

a(n) = [A034386(prime(n))/(2*A034386(prime(n)-2))], n>2. - [R. J. Mathar, May 18 2009]

MATHEMATICA

Table[Prime[n] - Floor[Prime[n]/2] - 1, {n, 65}] (* Robert G. Wilson v *)

PROG

(PARI) c(n, r) = { local(p); forprime(p=r, n, print1(floor(primorial(p)/ primorial(p-r)/primorial(r)+.0)", ") ) } primorial(n) = \ The product primes <= n using the pari primelimit. { local(p1, x); if(n==0||n==1, return(2)); p1=1; forprime(x=2, n, p1*=x); return(p1) }

CROSSREFS

Cf. A005097 [R. J. Mathar, May 18 2009]

Sequence in context: A274332 A130290 A005097 * A139791 A027563 A219729

Adjacent sequences:  A102778 A102779 A102780 * A102782 A102783 A102784

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Feb 25 2005

EXTENSIONS

Simpler definition from Giovanni Teofilatto, Nov 05 2005

Edited by N. J. A. Sloane Jul 05 2009 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)