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a(1)=3; thereafter, if n odd, a(n) = a(n-1)-st prime, and if n even, a(n) = a(n-1)-st nonprime.
3

%I #27 Mar 12 2017 16:29:02

%S 3,6,13,21,73,98,521,636,4721,5439,53323,59318,737183,801235,12215237,

%T 13068626,238205651,251987681,5381022817,5644769560,138933578143,

%U 144807081479,4053430178401,4203399920996,132332669898119,136669373292795,4793783797371011

%N a(1)=3; thereafter, if n odd, a(n) = a(n-1)-st prime, and if n even, a(n) = a(n-1)-st nonprime.

%C This is the sequence S_2 mentioned in A141436. The primes and nonprimes alternate.

%p # See A280028 for Maple program

%t nonPrime[n_Integer] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n]; a[n_] := a[n] = If[OddQ@ n, Prime@ a[n -1], nonPrime[ a[n -1]]]; a[1] = 3; Array[a, 26] *( _Robert G. Wilson v_, Dec 28 2016 *)

%Y Cf. A000040, A018252, A141436, A280028, A280030.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 25 2016

%E a(12)-a(26) from _Hans Havermann_, Dec 25 2016

%E a(27) from _Chai Wah Wu_, Dec 27 2016