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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; (3) k is not already in the sequence; and (4) |k-a(n)| is not the absolute difference of two previous consecutive members of the sequence.
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%I #7 Jan 14 2021 20:15:41

%S 1,3,6,23,4,9,2,45,8,67,56,123,34,5,78,7,234,1415,1234,1011,910,89,

%T 456,1213,12,2345,678,2425,3456,1819,123456,2627,45678,4445,101112,

%U 3031,5678,345,1516,789,1718,567,2728,100101,2324,4567,1314,891011,4344

%N 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; (3) k is not already in the sequence; and (4) |k-a(n)| is not the absolute difference of two previous consecutive members of the sequence.

%e 12 follows 23 as 23-12 = 11 is prime.

%Y Cf. A090911, A090912.

%K base,nonn,easy

%O 0,2

%A _Amarnath Murthy_, Dec 15 2003

%E Edited and extended by _David Wasserman_, Feb 14 2006