A201020 -id:A201020 - cp's OEIS frontend

A201019 Primes whose multiplicative digital root is 6.

23, 47, 61, 227, 281, 283, 347, 443, 449, 467, 487, 647, 683, 743, 769, 773, 797, 821, 823, 829, 863, 887, 967, 977, 1123, 1213, 1231, 1283, 1289, 1321, 1471, 1481, 1487, 1489, 1627, 1697, 1741, 1783, 1823, 1847, 1861, 1873, 2113, 2131, 2237, 2243, 2267, 2273, 2281, 2287, 2311

Offset: 1

Jaroslav Krizek, Nov 25 2011

Complement of A201020 with respect to A034053.

			Prime 227 is in sequence because 2*2*7=28, 2*8=16, 1*6=6.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A201020 (composite numbers whose multiplicative digital root is 6), A034053 (numbers whose multiplicative digital root is 6).

dr6Q[n_]:=NestWhile[Times@@IntegerDigits[#]&,n,#>9&]==6; Select[ Prime[ Range[ 400]],dr6Q] (* Harvey P. Dale, Jun 16 2016 *)

A201055 Composite numbers whose product of digits is 6.

Original entry on oeis.org

6, 16, 32, 116, 123, 132, 161, 213, 231, 312, 321, 611, 1116, 1132, 1161, 1312, 1611, 3112, 3211, 6111, 11116, 11123, 11132, 11231, 11312, 11611, 12131, 12311, 13112, 13211, 21113, 21131, 21311, 23111, 31112, 31211, 32111, 61111, 111116, 111123, 111132, 111161

Offset: 1

Jaroslav Krizek, Nov 26 2011

			Number 123 is in sequence because 1*2*3 = 6.

Michael S. Branicky, Table of n, a(n) for n = 1..10860 (all terms with <= 32 digits)

Cf. A199988 (numbers whose product of digits is 6).
Complement of A107692 (primes whose product of digits is 6) with respect to A199988.
Subsequence of A201020 (composite numbers whose multiplicative digital root is 6).

from sympy import prod, isprime
from sympy.utilities.iterables import multiset_permutations
def agen(maxdigits):
    for digs in range(1, maxdigits+1):
        for mp in multiset_permutations("1"*(digs-1) + "236", digs):
            if prod(map(int, mp)) == 6:
                t = int("".join(mp))
                if not isprime(t): yield t
print(list(agen(6))) # Michael S. Branicky, Jun 16 2021

cp's OEIS Frontend

A201019 Primes whose multiplicative digital root is 6.

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