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Numbers k such that the product of decimal digits of k divides k+1.
1

%I #14 Jul 25 2024 15:15:57

%S 1,11,21,23,27,111,113,121,131,143,161,167,211,233,311,323,411,431,

%T 447,539,611,671,713,863,1111,1121,1133,1147,1211,1217,1223,1259,1313,

%U 1331,1411,1529,1619,1637,1721,1763,1823,1943,2111,2123,2127,2159,2211,2231

%N Numbers k such that the product of decimal digits of k divides k+1.

%H Nathaniel Johnston, <a href="/A178413/b178413.txt">Table of n, a(n) for n = 1..1000</a>

%p A178413 := proc(n) option remember: local k,q: if(n=1)then return 1: fi: for k from procname(n-1)+1 do q:=mul(d,d=convert(k,base,10)): if(q>0 and k+1 mod q = 0)then return k: fi: od: end: seq(A178413(n),n=1..48); # _Nathaniel Johnston_, May 27 2011

%t Select[Range[2500],FreeQ[IntegerDigits[#],0]&&Mod[#+1,Times@@IntegerDigits[#]]==0&] (* _Harvey P. Dale_, Jul 25 2024 *)

%Y Cf. A007602.

%K nonn,base

%O 1,2

%A _Giovanni Teofilatto_, May 27 2010

%E More terms from _R. J. Mathar_, May 28 2010