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Search: id:A102781
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| A102781 |
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Number of even numbers less than the n-th prime. |
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+0
9
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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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Same as A005097 ((odd primes - 1)/2) with a leading zero. (Lambert Klasen, Nov 06 2005)
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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 (hillcino368(AT)gmail.com), Feb 25 2005
a(n) = prime_n - floor((prime_n)/2) - 1. Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), 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 (mathar(AT)strw.leidenuniv.nl), May 18 2009]
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MATHEMATICA
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Table[Prime[n] - Floor[Prime[n]/2] - 1, {n, 65}] (* Robert G. Wilson v *)
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PROGRAM
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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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Cf. A005097 [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2009]
Sequence in context: A130290 A161719 A005097 this_sequence A139791 A147855 A027563
Adjacent sequences: A102778 A102779 A102780 this_sequence A102782 A102783 A102784
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Feb 25 2005
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EXTENSIONS
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Simpler definition from Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Nov 05 2005
Edited by N. J. A. Sloane Jul 05 2009 at the suggestion of R. J. Mathar
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