%I #38 Jan 02 2022 19:22:25

%S 10,12,20,21,23,24,30,32,34,36,40,42,43,45,46,48,50,54,56,60,63,64,65,

%T 67,68,69,70,76,78,80,84,86,87,89,90,96,98,100,105,108,120,121,126,

%U 128,162,200,240,242,300,324,325,350,360,363,400,405,450,480,484,500,560,564,589,600,612,648,700,728,748,750

%N Numbers k with the property that concatenating all successive absolute differences between two successive digits of k produces a divisor of k.

%C To avoid having to consider divisors with leading zeros, we require that the first two digits of k be distinct.

%C There is no 10-digit pandigital with this property. The closest 9-digit one is 349186750.

%H Harvey P. Dale, <a href="/A338640/b338640.txt">Table of n, a(n) for n = 1..300</a>

%e The number k = 349186750 mentioned in the Comments section produces the successive absolute differences:

%e |3 - 4| = 1

%e |4 - 9| = 5

%e |9 - 1| = 8

%e |1 - 8| = 7

%e |8 - 6| = 2

%e |6 - 7| = 1

%e |7 - 5| = 2

%e |5 - 0| = 5

%e ... and the integer 15872125 (visible in the right column) is indeed a divisor of k (349186750/15872125 = 22).

%t cadQ[n_]:=Module[{idn=Abs[Differences[IntegerDigits[n]]]},idn[[1]]!=0 && Divisible[n,FromDigits[idn]]]; Select[Range[10,800],cadQ]//Quiet (* _Harvey P. Dale_, Jan 02 2022 *)

%Y Cf. A338855 [the concatenation is a subchain of k], A338641 (the digits of k are all distinct).

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Nov 13 2020

%E Definition clarified by _N. J. A. Sloane_, Jan 02 2022 at the suggestion of _Harvey P. Dale_.