A069196 a(1)=1, a(2)=3; for n>1, a(n+2)=(a(n+1)+a(n))/3 if (a(n+1)+a(n)==0 (mod 3)); a(n+2)=(a(n+1)+a(n))/2 if (a(n+1)+a(n)==0 (mod 2)); and a(n+2)=a(n+1)+a(n) otherwise.

1, 3, 2, 5, 7, 4, 11, 5, 8, 13, 7, 10, 17, 9, 13, 11, 8, 19, 9, 14, 23, 37, 20, 19, 13, 16, 29, 15, 22, 37, 59, 32, 91, 41, 44, 85, 43, 64, 107, 57, 82, 139, 221, 120, 341, 461, 401, 431, 416, 847, 421, 634, 1055, 563, 809, 686, 1495, 727, 1111, 919, 1015, 967, 991