%I #11 Jan 14 2023 12:41:47
%S 1,1,2,1,3,2,3,4,4,5,5,6,6,7,7,8,8,9,10,11,9,12,13,10,14,15,16,17,11,
%T 12,18,19,13,14,20,21,22,23,15,24,25,26,27,28,29,16,30,31,17,18,32,33,
%U 34,35,36,37,19,20,38,39,40,41,21,42,43,22,44,45,46,47,23,24,48,49,50,51
%N a(n+1) = if a(n) is prime then (number of primes so far) else (number of nonprimes so far), a(1) = 1.
%C All terms greater than 1 occur exactly twice: a(A137662(n)) = a(n).
%H Reinhard Zumkeller, <a href="/A137661/b137661.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n+1) = A005171(a(n))*Sum(A005171(a(k)):1<=k<=n) + A010051(a(n))*Sum(A010051(a(k)):1<=k<=n).
%p A137661 := proc(n)
%p option remember;
%p if n = 1 then
%p 1;
%p else
%p A005171(procname(n-1)) * add(A005171(procname(k)),k=1..n-1)
%p +A010051(procname(n-1)) * add(A010051(procname(k)),k=1..n-1)
%p end if;
%p end proc: # _R. J. Mathar_, Sep 27 2021
%t nn = 120; k = 1; q = 1; Prepend[Array[Set[k, If[PrimeQ[k], # - q, q++]] &, nn - 1, 2], 1] (* _Michael De Vlieger_, Jan 14 2023 *)
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, Feb 04 2008