A371281 -id:A371281 - cp's OEIS frontend

A371222 Product of digits of (n written in base 3) mod 3.

0, 1, 2, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Ctibor O. Zizka, Mar 18 2024

a(A032924(n)) = 1 or 2. For n >= 1, a(A032924(n)) - 1 = A309953(A032924(n)) mod 3 - 1 = A010059(n+1).

			n = 5: 5_10 = 12_3 thus a(5) = 1*2 mod 3 = 2.
n = 8: 8_10 = 22_3 thus a(8) = 2*2 mod 3 = 1.

Cf. A007089, A010059, A032924, A081605, A309953, A371281 (base 10).

a[n_] := Mod[Times @@ IntegerDigits[n, 3], 3]; Array[a, 100, 0] (* Amiram Eldar, Mar 18 2024 *)

from functools import reduce
from sympy.ntheory import digits
def A371222(n): return reduce(lambda a,b: a*b%3,digits(n,3)[1:],1) # Chai Wah Wu, Mar 19 2024

a(n) = A309953(n) mod 3.

a(A081605(n)) = 0.

A382402 Numbers divisible by the product of their digits (mod 10).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 26, 34, 35, 37, 48, 55, 62, 64, 66, 72, 73, 75, 76, 78, 84, 88, 95, 96, 98, 99, 111, 112, 115, 126, 132, 134, 135, 136, 137, 144, 148, 155, 162, 164, 168, 172, 173, 175, 176, 184, 188, 192, 195, 196, 198, 199, 212, 216, 228, 232, 244, 248, 264, 266

Offset: 1

Enrique Navarrete, Mar 23 2025

Unlike A007602 and A064700, where there are no other primes besides 2, 3, 5, 7 and primes with repunits, this sequence contains other primes such as 37, 73 and 137.

The sequence has asymptotic density 0, since it contains no numbers with digit 5 and an even digit. - Robert Israel, Jun 01 2025

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007602, A064700, A371281.

filter:= proc(n) local L,t;
  L:= convert(n,base,10);
  t:= convert(L,`*`) mod 10;
  t > 0 and n mod t = 0
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 01 2025

Select[Range[300], (prod = Mod[Times @@ IntegerDigits[#], 10]) > 0 && Divisible[#, prod] &] (* Amiram Eldar, Mar 23 2025 *)

isok(k) = my(p=lift(vecprod(apply(x->Mod(x, 10), digits(k))))); if (p, !(k % p)); \\ Michel Marcus, Mar 31 2025

from math import prod
def ok(n): return (p:=prod(map(int, str(n)))%10) > 0 and n%p == 0
print([k for k in range(300) if ok(k)]) # Michael S. Branicky, Mar 23 2025

cp's OEIS Frontend

A371222 Product of digits of (n written in base 3) mod 3.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Python

Formula