A090911 a(n+1) is the least positive integer k such that 1) k is a one-digit number or the concatenation of two or more consecutive numbers; 2) |k-a(n)| is prime; and 3) |k-a(n)| is not the absolute difference of two previous consecutive members of the sequence.

1, 3, 6, 1, 8, 45, 2, 789, 56, 3, 34, 5, 78, 7, 234, 1, 12, 1213, 456, 7, 1314, 23, 4, 45, 1516, 5, 234, 23, 6, 67, 8, 345, 34, 123, 56, 9, 1112, 3, 910, 23, 456, 67, 234, 1415, 6, 89, 456, 2345, 4, 567, 1718, 9, 2122, 23, 1516, 89, 910, 1011, 2, 2223, 10111012, 1415