%I
%S 10,13,14,15,16,17,18,19,90,100,101,102,103,104,105,106,107,108,109,
%T 133,132,131,130,137,138,139,207,208,209,144,143,142,141,140,149,306,
%U 307,308,309,155,154,153,152,151,150,260,370,408,409,166,165,164,163,162,161,160,270
%N The minimum number such that the concatenation of the absolute values of differences between adjacent digits of a(n) is n. Values of n which have no such a(n) are given as 1.
%C This sequence gives the minimum value such that the concatenation of the absolute value of the differences between its adjacent digits give n. Some values of n have no ancestor, see A271639. These are given the value 1 in this sequence.
%e a(1) = 10 as 1  0 = 1, and 10 is the smallest such number.
%e a(9) = 90 as 9  0 = 9, and 90 is the smallest such number
%e a(10) = 100 as 1  0 = 1, and 0  0 = 0, giving a concatenation of 10. 100 is the smallest such number.
%e a(48) = 408 as 4  0 = 4 and 0  8 = 8, giving a concatenation of 48. 408 is the smallest such number.
%t max = 60; seq = Table[1, {max}]; count = 0; n = 1; While[count < max && n <= 10^(1 + Ceiling[Log10[max]]), index = FromDigits @ Abs @ Differences @ IntegerDigits[n]; If[index <= max && seq[[index]] < 0, count++; seq[[index]] = n]; n++]; seq (* _Amiram Eldar_, Nov 29 2019 *)
%Y Cf. A271639, A040115.
%K nonn,base
%O 1,1
%A _Scott R. Shannon_, Nov 29 2019
