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.

10, 20, 30, 40, 50, 60, 70, 80, 90, 12, 21, 23, 32, 24, 42, 34, 43, 36, 63, 45, 54, 46, 64, 48, 84, 56, 65, 67, 76, 68, 86, 69, 96, 78, 87, 89, 98, 120, 105, 108, 240, 350, 360, 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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..108.

Example

The last integer of the list 349186750 produces the successive absolute differences:
|3 - 4| = 1
|4 - 9| = 5
|9 - 1| = 8
|1 - 8| = 7
|8 - 6| = 2
|6 - 7| = 1
|7 - 5| = 2
|5 - 0| = 5
... and the integer 15872125 (visible in the right column) is indeed a divisor of the starting number (349186750/15872125 = 22).

Crossrefs

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

Sequence in context: A037997 A044850 A282150 * A337857 A044895 A370400

Adjacent sequences: A338638 A338639 A338640 * A338642 A338643 A338644

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Nov 13 2020

Status

approved