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The four digits of a(n), their three successive absolute first differences and their two successive absolute second differences are all distinct.
1

%I #23 Nov 23 2023 11:25:52

%S 2983,3892,4197,4917,5298,5928,7194,7398,7914,7938,8139,8295,8329,

%T 8397,8925,8937,9238,9318

%N The four digits of a(n), their three successive absolute first differences and their two successive absolute second differences are all distinct.

%C The digit 0 is never present in a(n) and never appears as a first or a second difference (as this would duplicate in both cases one of the 8 remaining digits involved).

%C The sequence ends with a(18) = 9318.

%e 2983 is a term since its three successive absolute first differences 7 (= 2 - 9), 1 (= 9 - 8), 5 (= 8 - 3) and the successive absolute second differences 6 (= 7 - 1) and 4 (= 1 - 5), are nine distinct digits.

%e 2 9 8 3

%e 7 1 5

%e 6 4

%t Select[Range[1000,9999],Sort@Join[IntegerDigits@#, s=Abs@Differences@IntegerDigits@#, Abs@Differences@s]==Range@9&]

%Y Cf. A365257, A100787, A040114, A270263.

%K base,nonn,fini,full

%O 1,1

%A _Eric Angelini_ and _Giorgos Kalogeropoulos_, Aug 29 2023