A338641 - OEIS

A338641

Positive integers k having no duplicated digit such that concatenating all successive absolute differences between two successive digits of k produces a divisor of k.

%I #28 Nov 15 2020 12:54:54

%S 10,20,30,40,50,60,70,80,90,12,21,23,32,24,42,34,43,36,63,45,54,46,64,

%T 48,84,56,65,67,76,68,86,69,96,78,87,89,98,120,105,108,240,350,360,

%U 405,450,480,560,750,126,162,612,128,324,325,923,728,564,648,748,784,756,589,768,798,1240,1350,2480,3450,4309,6450,6750,7560,8750,9805,7680,1623,4512,2196,9821,4318,3429,4329,6528,9728,4356,6534,5687,7865,12480,21078,34086,46750,96450,56129,76328,67984,451608,538209,965402,954086,428176,691578,873642,3574192,41509836,98016534,83574192,349186750

%N Positive integers k having no duplicated digit such that concatenating all successive absolute differences between two successive digits of k produces a divisor of k.

%C There are only 108 integers with this property: they are all listed above.

%e The last integer of the list 349186750 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 the starting number (349186750/15872125 = 22).

%Y Cf. A338855 and A338640 (variants on the same idea).

%K base,nonn

%O 1,1

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