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A142351
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Primes of the form k/(3*(c(k)-r(k))), where c(k) = k-th composite and r(k) = k-th nonprime.
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1
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3, 13, 11, 17, 29, 31, 23, 41, 43, 53, 61, 41, 43, 67, 47, 71, 73, 79, 83, 67, 101, 107, 109, 113, 79, 137, 139, 97, 149, 101, 157, 107, 167, 173, 179, 127, 191, 193, 197, 199, 139, 211, 223, 151, 227, 229, 241, 167, 251, 179, 269, 271, 277, 281, 283, 307, 311, 317
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OFFSET
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1,1
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LINKS
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EXAMPLE
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For k=18, 18/(3*(c(18)-r(18))=6/(28-26)=3=a(1).
For k=78, 78/(3*(c(78)-r(78))=26/(106-104)=13=a(2).
For k=99, 99/(3*(c(99)-r(99))=33/(132-129)=11=a(3).
For k=102, 102/(3*(c(102)-r(102))=34/(135-133)=17=a(4).
For k=174, 174/(3*(c(174)-r(174))=58/(222-220)=29=a(5).
For k=186, 186/(3*(c(186)-r(186))=62/(238-236)=31=a(6).
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MAPLE
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A141468 := proc(n) option remember ; if n = 1 then 0; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end: A002808 := proc(n) option remember ; A141468(n+2) ; end: for n from 1 to 3000 do p := n/(A002808(n)-A141468(n))/3 ; if type(p, 'integer') then if isprime(p) then printf("%d, ", p) ; fi; fi; od: # R. J. Mathar, Jan 23 2009
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MATHEMATICA
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A141468 [n_] := A141468[n] = If[n == 1, 0, For[a = A141468[n - 1] + 1, True, a++, If[!PrimeQ[a], Return[a]]]];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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