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%I #8 Aug 07 2015 02:49:11
%S 1,5,7,10,16,24,33,43,48,60,74,89,96,112,130,150,171,193,204,228,253,
%T 279,306,334,364,396,429,463,476,511,547,564,602,641,660,700,742,786,
%U 831,877,900,948,997,1026,1076,1127,1179,1233,1288,1344,1401,1459,1490
%N a(1)=1. a(n)=a(n-1)+k(n). If a(n-1) is nonprime, k(n) is the smallest composite not in the set {k(i),i<n}. If a(n-1) is prime, k(n) is the smallest prime not in the set {k(i),i<n}.
%e a(2) = 1+4 = 5 which is prime hence a(3) = 5+2 = 7 which is also a prime,a(4)= 7+3 = 10 which is composite hence a(5) = 10 + 6 = 16.
%p A073895 :=proc(nmax) local a,kset; a := [1] ; kset := {} ; while nops(a) < nmax do k :=2; while k in kset or isprime(k)<>isprime(op(-1,a)) do k := k+1 ; od ; a := [op(a),op(-1,a)+k] ; kset := kset union {k} ; od ; RETURN(a) ; end: op(A073895(80)) ; # _R. J. Mathar_, Jun 27 2007
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, Aug 18 2002
%E More terms from _R. J. Mathar_, Jun 27 2007