A152826 Numbers that are divisible by the product of the digit-sums of their neighbors.

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

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