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A152826 Numbers that are divisible by the product of the digit-sums of their neighbors. 1
105, 672, 1200, 1530, 1560, 2145, 2907, 3060, 3432, 4704, 5814, 6006, 6120, 6240, 8721, 9570, 10710, 10752, 10920, 11154, 11628, 11700, 12240, 12441, 13260, 14535, 15015, 16302, 17442, 19656, 20163, 20280, 20832, 21420, 22620, 23256, 23400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms are multiples of 3. Up to 10^8 there are exactly 6865 odd and 25055 even terms. - Zak Seidov, May 11 2013

Note the linear patterns in my jpg file. - Zak Seidov, May 11 2013

Subsequences include 10^(2+6k)+5, 10^(3+16k)+530, 10^(3+6k)+560, 2*10^(3+6k)+145, 2*10^(3+144k)+907, etc. - Robert Israel, Jan 05 2016

REFERENCES

Die WURZEL - Zeitschrift für Mathematik, 42. Jahrgang, Dezember 2008, Seite 287, WURZEL-Aufgabe sigma55 von Reiner Moewald, Germersheim.

LINKS

Robert Israel, Table of n, a(n) for n = 1..1000

Zak Seidov, plot of a(n)/3/A007953 (a(n) - 1)/A007953 (a(n) + 1) for n=1..31920.

MAPLE

ds:= n -> convert(convert(n, base, 10), `+`):

filter:= n -> n mod (ds(n-1)*ds(n+1))=0:

select(filter, 3*[$1..10000]); # Robert Israel, Jan 05 2016

MATHEMATICA

Select[Range[50000], Divisible[#, Total[IntegerDigits[#-1]] * Total[IntegerDigits[#+1]]]&] (* Harvey P. Dale, Dec 11 2010 *)

PROG

(Java) class Program { static void Main(string[] args) { for (int i = 1; i < 1000000; i++) { int q1 = quersumme(i - 1); int q2 = quersumme(i + 1); if ((double)i % ((double)q1 * (double)q2) == 0) { Console.WriteLine(i); } } Console.ReadLine(); } static int quersumme(int num) { string n = num.ToString(); int retval = 0; int i = n.Length - 1; while (i >= 0) { retval += Int32.Parse(n.Substring(i, 1)); i--; } return retval; } }

CROSSREFS

Cf. A007953.

Sequence in context: A200834 A143041 A078420 * A133767 A166816 A166798

Adjacent sequences: A152823 A152824 A152825 * A152827 A152828 A152829

KEYWORD

nonn,base,easy

AUTHOR

Gerhard Palme (GerhardPalme(AT)gmx.de), Dec 13 2008

STATUS

approved

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Last modified November 27 14:32 EST 2022. Contains 358405 sequences. (Running on oeis4.)