A142351 - OEIS

%I #20 Oct 01 2024 07:26:28

%S 3,13,11,17,29,31,23,41,43,53,61,41,43,67,47,71,73,79,83,67,101,107,

%T 109,113,79,137,139,97,149,101,157,107,167,173,179,127,191,193,197,

%U 199,139,211,223,151,227,229,241,167,251,179,269,271,277,281,283,307,311,317

%N Primes of the form k/(3*(c(k)-r(k))), where c(k) = k-th composite and r(k) = k-th nonprime.

%H Robert Israel, <a href="/A142351/b142351.txt">Table of n, a(n) for n = 1..10000</a>

%e For k=18, 18/(3*(c(18)-r(18)))=6/(28-26)=3=a(1).

%e For k=78, 78/(3*(c(78)-r(78)))=26/(106-104)=13=a(2).

%e For k=99, 99/(3*(c(99)-r(99)))=33/(132-129)=11=a(3).

%e For k=102, 102/(3*(c(102)-r(102)))=34/(135-133)=17=a(4).

%e For k=174, 174/(3*(c(174)-r(174)))=58/(222-220)=29=a(5).

%e For k=186, 186/(3*(c(186)-r(186)))=62/(238-236)=31=a(6).

%p 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

%t A141468 [n_] := A141468[n] = If[n == 1, 0, For[a = A141468[n - 1] + 1, True, a++, If[!PrimeQ[a], Return[a]]]];

%t A002808[n_] := A002808[n] = A141468[n + 2];

%t 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_ *)

%Y Cf. A002808, A141468, A161811.

%K nonn,look

%O 1,1

%A _Juri-Stepan Gerasimov_, Sep 21 2008

%E Corrected and extended by _R. J. Mathar_, Jan 23 2009

%E Edited by _Robert Israel_, Mar 15 2019