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A102781
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Number of positive even numbers less than the n-th prime.
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12
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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
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OFFSET
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1,3
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COMMENTS
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Same as A005097 ((odd primes - 1)/2) with a leading zero. - Lambert Klasen, Nov 06 2005
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LINKS
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FORMULA
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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)-1)/2] where the integer part [.] needs be taken only for n=1. - M. F. Hasler, Dec 13 2019
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MATHEMATICA
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PROG
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(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) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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