A324321 - OEIS

%I #9 Mar 14 2019 09:23:05

%S 21,23,25,27,29,31,34,37,41,45,49,51,56,61,67,71,78,81,89,91,101,109,

%T 114,118,145,175,201,209,251,267,301,365,401,501,529,601,701,801,901,

%U 1001,1639,2001,3001,4001,5001,6001,7001,8001,9001,10001,20001,30001,40001

%N Numbers k such that Rd(k) == k (mod Ld(k)), where Rd(k) = A067079 and Ld(k) = A067080.

%C All numbers of the form d*10^k+1, where d = 1,2,3,4,5,6,7,8,9 and k>0, are part of the sequence except 11.

%e Rd(1639) = 1639*639*39*9 = 367609671, Ld(1639) = 1639*163*16*1 = 4274512 and 367609671 == 1639 (mod 4274512).

%p op(select(n->n=mul(n mod 10^k, k=1..ilog10(n)+1) mod mul(trunc(n/10^k), k=0..ilog10(n)),[$1..40001]));

%t Select[Range[10^5], Mod[Times @@ Map[FromDigits, NestWhileList[Rest@ # &, IntegerDigits@ #, Length@ # > 1 &]], Times @@ Map[FromDigits, NestWhileList[Most@ # &, IntegerDigits@ #, Length@ # > 1 &]]] == # &] (* _Michael De Vlieger_, Feb 25 2019 *)

%Y Cf. A067079, A067080, A324322.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Feb 22 2019