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A338640
Numbers k with the property that concatenating all successive absolute differences between two successive digits of k produces a divisor of k.
3
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
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
KEYWORD
base,nonn
AUTHOR
EXTENSIONS
Definition clarified by N. J. A. Sloane, Jan 02 2022 at the suggestion of Harvey P. Dale.
STATUS
approved