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A280028 a(1)=1; thereafter, if n even, a(n) = a(n-1)-st prime, and if n odd, a(n) = a(n-1)-st nonprime.

%I A280028 #31 Dec 28 2016 10:05:12
%S A280028 1,2,4,7,12,37,52,239,301,1993,2338,20753,23356,266587,291968,4134187,
%T A280028 4446630,75947059,80652283,1625456353,1710094788,39954587527,
%U A280028 41737658509,1114336791787,1157634258442,34900173534517,36096139358620,1216553712004063
%N A280028 a(1)=1; thereafter, if n even, a(n) = a(n-1)-st prime, and if n odd, a(n) = a(n-1)-st nonprime.
%C A280028 This is the sequence S_1 mentioned in A141436. The primes and nonprimes alternate.
%p A280028 P:=n->ithprime(n);
%p A280028 # let b1 be a list of the nonprimes (from the b-file for A018252)
%p A280028 N:=n->if n<=nops(b1) then b1[n] else 0; fi;;
%p A280028 f:=proc(m) local S,n,sw,t; global P,N;
%p A280028 S:=[m]; t:=m;
%p A280028    if isprime(m) then sw:=1; else sw:=2; fi;
%p A280028 if sw=1 then
%p A280028    for n from 2 to 60 do
%p A280028    if n mod 2 = 0 then t:=N(t); if t=0 then return(S); fi; else t:=P(t); fi; S:=[op(S),t];
%p A280028    od:
%p A280028 else
%p A280028    for n from 2 to 60 do
%p A280028    if n mod 2 = 0 then t:=P(t); else t:=N(t); if t=0 then return(S); fi; fi; S:=[op(S),t];
%p A280028    od:
%p A280028 fi;
%p A280028 S;
%p A280028 end;
%p A280028 f(1); # A280028
%p A280028 f(3); # A280029
%p A280028 f(5); # A280030
%t A280028 nonPrime[n_Integer] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n]; a[n_] := If[ OddQ@ n, nonPrime[ a[n -1]], Prime@a[n -1]]; a[1] = 1; Array[a, 26] (* _Robert G. Wilson v_, Dec 28 2016 *)
%Y A280028 Cf. A000040, A018252, A141436, A280029, A280030.
%K A280028 nonn
%O A280028 1,2
%A A280028 _N. J. A. Sloane_, Dec 25 2016
%E A280028 a(13)-a(27) from _Hans Havermann_, Dec 25 2016
%E A280028 a(28) from _Chai Wah Wu_, Dec 26 2016