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A139637 If n = the k-th prime, then a(n) = the (k-1)th prime. If n = the k-th composite, then a(n) = the (k-1)th composite. a(2) = 1. a(4) = 0.

%I A139637 #16 Jul 04 2025 19:22:11
%S A139637 1,2,0,3,4,5,6,8,9,7,10,11,12,14,15,13,16,17,18,20,21,19,22,24,25,26,
%T A139637 27,23,28,29,30,32,33,34,35,31,36,38,39,37,40,41,42,44,45,43,46,48,49,
%U A139637 50,51,47,52,54,55,56,57,53,58,59,60,62,63,64,65,61,66,68,69,67,70,71,72
%N A139637 If n = the k-th prime, then a(n) = the (k-1)th prime. If n = the k-th composite, then a(n) = the (k-1)th composite. a(2) = 1. a(4) = 0.
%C A139637 This is a permutation of the nonnegative integers.
%p A139637 A000040 := proc(n) ithprime(n) ; end: A002808 := proc(n) local a; if n = 1 then 4; else for a from A002808(n-1)+1 do if not isprime(a) then RETURN(a) ; fi ; od: fi ; end: A066246 := proc(n) local k ; if isprime(n) then 0 ; else for k from 1 do if A002808(k) = n then RETURN(k) ; fi ; od: fi ; end: A049084 := proc(n) if not isprime(n) then 0; else numtheory[pi](n) ; fi ; end: A139637 := proc(n) local k; if n = 2 then 1; elif n = 4 then 0 ; else if isprime(n) then k := A049084(n) ; A000040(k-1) ; else k := A066246(n) ; A002808(k-1) ; fi ; fi ; end: seq(A139637(n),n=2..160) ; # _R. J. Mathar_, May 12 2008
%t A139637 HC[k_] := If[k <= 4, None, Max[Select[Range[4, k-1], !PrimeQ[#]&]]];a[2]=1;a[4]=0;a[n_]:=If[PrimeQ[n],Prime[PrimePi[n-1]],HC[n]];Array[a,73,2] (* _James C. McMahon_, Jul 01 2025 *)
%Y A139637 Cf. A000040, A002808, A139636.
%K A139637 nonn
%O A139637 2,2
%A A139637 _Leroy Quet_, Apr 28 2008
%E A139637 More terms from _R. J. Mathar_, May 12 2008