A152826 - OEIS

%I #27 Jan 06 2016 11:46:45

%S 105,672,1200,1530,1560,2145,2907,3060,3432,4704,5814,6006,6120,6240,

%T 8721,9570,10710,10752,10920,11154,11628,11700,12240,12441,13260,

%U 14535,15015,16302,17442,19656,20163,20280,20832,21420,22620,23256,23400

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

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

%C Note the linear patterns in my jpg file. - _Zak Seidov_, May 11 2013

%C 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

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

%H Robert Israel, <a href="/A152826/b152826.txt">Table of n, a(n) for n = 1..1000</a>

%H Zak Seidov, plot of <a href="/A152826/a152826.jpg">a(n)/3/A007953 (a(n) - 1)/A007953 (a(n) + 1)</a> for n=1..31920.

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

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

%p select(filter, 3*[$1..10000]); # _Robert Israel_, Jan 05 2016

%t Select[Range[50000], Divisible[#,Total[IntegerDigits[#-1]] * Total[IntegerDigits[#+1]]]&] (* _Harvey P. Dale_, Dec 11 2010 *)

%o (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; } }

%Y Cf. A007953.

%K nonn,base,easy

%O 1,1

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