A338640 Numbers k with the property that concatenating all successive absolute differences between two successive digits of k produces a divisor of k.

10, 12, 20, 21, 23, 24, 30, 32, 34, 36, 40, 42, 43, 45, 46, 48, 50, 54, 56, 60, 63, 64, 65, 67, 68, 69, 70, 76, 78, 80, 84, 86, 87, 89, 90, 96, 98, 100, 105, 108, 120, 121, 126, 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

Offset

1,1

Comments

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

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..300

Example

The number k = 349186750 mentioned in the Comments section 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 k (349186750/15872125 = 22).

Mathematica

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 *)

Crossrefs

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

Sequence in context: A038527 A270263 A048378 * A129845 A075492 A225742

Adjacent sequences: A338637 A338638 A338639 * A338641 A338642 A338643

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Nov 13 2020

Extensions

Definition clarified by N. J. A. Sloane, Jan 02 2022 at the suggestion of Harvey P. Dale.

Status

approved