A142351 Primes of the form k/(3*(c(k)-r(k))), where c(k) = k-th composite and r(k) = k-th nonprime.
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
Offset: 1
Examples
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).
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
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
A141468 [n_] := A141468[n] = If[n == 1, 0, For[a = A141468[n - 1] + 1, True, a++, If[!PrimeQ[a], Return[a]]]]; A002808[n_] := A002808[n] = A141468[n + 2]; Reap[For[n = 1, n <= 3000, n++, p = n/(A002808[n] - A141468[n])/3; If[PrimeQ[p], Sow[p]]]][[2, 1]] (* Jean-François Alcover, Aug 28 2020, after R. J. Mathar *)
Extensions
Corrected and extended by R. J. Mathar, Jan 23 2009
Edited by Robert Israel, Mar 15 2019