A089562 a(1) = 7. For n > 1, a(n) is the least unused number such that every concatenation a(n)a(n-1)...a(2)a(1) is prime.

7, 1, 3, 6, 2, 21, 10, 9, 8, 37, 20, 25, 29, 72, 28, 30, 27, 23, 39, 19, 51, 32, 22, 54, 42, 35, 24, 73, 36, 120, 44, 186, 4, 26, 126, 171, 70, 33, 18, 60, 113, 99, 81, 76, 47, 108, 91, 170, 159, 49, 65, 114, 238, 185, 285, 34, 98, 312, 63, 183, 15, 205, 230, 198, 310, 524