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 A102781 Number of positive even numbers less than the n-th prime. 12
 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 n# = product of primes <= n. 0# = 1# = 2. [This is not a standard convention!] n#/(n-r)#/r# is analogous to the number of binomial coefficients A007318 = C(n, r) = n!/(n-r)!/r! where factorial ! is replaced by primorial #. a(n) = prime_n - floor((prime_n)/2) - 1. - Giovanni Teofilatto, Nov 05 2005 a(n) = [A034386(prime(n))/(2*A034386(prime(n)-2))], n>2. - R. J. Mathar, May 18 2009 a(n) = [(prime(n)-1)/2] where the integer part [.] needs be taken only for n=1. - M. F. Hasler, Dec 13 2019 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) } (PARI) apply( A102781(n)=(prime(n)-1)\2, [1..99]) \\ M. F. Hasler, Dec 13 2019 CROSSREFS Cf. A005097. - R. J. Mathar, May 18 2009 Equals (A000040-1)/2, integer part (0) for the first term. - M. F. Hasler, Dec 13 2019 Sequence in context: A082583 A274332 A005097 * A130290 A139791 A027563 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 July 12 12:18 EDT 2020. Contains 335661 sequences. (Running on oeis4.)