A324322 Numbers k such that Ld(k) == k (mod Rd(k)), where Ld(k) = A067080 and Rd(k) = A067079.

12, 13, 14, 15, 16, 17, 18, 19, 32, 43, 52, 54, 65, 72, 73, 76, 87, 92, 94, 98, 103, 352, 461, 571, 792, 803, 1003

Offset: 1

Author

Paolo P. Lava, Feb 22 2019

Keywords

• nonn
• more

Comments

No other term up to 2*10^10. - Giovanni Resta, Feb 22 2019

Examples

			Ld(792) = 792*79*7 = 437976, Rd(792) = 792*92*2 = 145728 and 437976 == 792 (mod 145728).
		

Crossrefs

Cf. A067079, A067080, A324322.

Programs

Maple

with(numtheory): P:=proc(n) local a,k;
a:=mul(n mod 10^k, k=1..ilog10(n)+1): if a>0 then
if n=mul(trunc(n/10^k), k=0..ilog10(n)) mod a then n;
fi; fi; end: seq(P(i),i=1..1100);

Mathematica

Select[Range[10^6], If[#2 != 0, Mod[Times @@ Map[FromDigits, NestWhileList[Most@ # &, IntegerDigits@ #1, Length@ # > 1 &]], #2] == #1] & @@ {#, Times @@ Map[FromDigits, NestWhileList[Rest@ # &, IntegerDigits@ #, Length@ # > 1 &]]} &] (* Michael De Vlieger, Feb 25 2019 *)

PARI

Ld(n) = my(t=n); while(n\=10, t*=n); t; \\ A067080
Rd(n) = prod(k=1, logint(n+!n, 10)+1, n-n\10^k*10^k); \\ A067079
isok(k) = if (k % 10, (Ld(k) % Rd(k)) == k); \\ Michel Marcus, Jan 15 2023