A277856 - OEIS

%I #15 Jan 07 2023 12:05:23

%S 1,2,3,4,5,6,7,8,9,11,111,212,216,612,1111,1113,1131,1311,2112,3111,

%T 4224,4416,6144,11111,11133,11313,11331,11711,13113,13131,13311,21112,

%U 21132,21312,23112,23424,31113,31131,31311,33111,42432,42624,111111,211112,211116

%N Numbers k such that the product of their digits divides both k and R(k), where R(k) is the digits reverse of k.

%C Subsequence of A007602.

%H David A. Corneth, <a href="/A277856/b277856.txt">Table of n, a(n) for n = 1..1228</a> (first 200 terms from Paola P. Lava, terms < 10^13)

%p R:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:

%p P:=proc(q) local a,n; for n from 1 to q do a:=convert(convert(n,base,10),`*`);

%p if a>0 then if R(n) mod a=0 and n mod a=0 then print(n); fi; fi; od; end: P(10^12);

%t pddQ[n_]:=Module[{pd=Times@@IntegerDigits[n]},pd!=0&&Mod[n,pd] == Mod[ IntegerReverse[n],pd]==0]; Select[Range[22*10^4],pddQ] (* _Harvey P. Dale_, Jan 07 2023 *)

%o (PARI) is(n) = { my(d = digits(n), vp = vecprod(d)); if(vp != 0 && n%vp == 0 && fromdigits(Vecrev(d))%vp == 0, return(1) ); 0 } \\ _David A. Corneth_, Mar 30 2021

%Y Cf. A004086, A007602.

%K nonn,base,easy

%O 1,2

%A _Paolo P. Lava_, Nov 02 2016