A199981 -id:A199981 - cp's OEIS frontend

A199980 Primes whose multiplicative digital root is 2.

2, 37, 43, 73, 137, 173, 211, 223, 317, 367, 389, 431, 673, 827, 839, 929, 983, 1223, 1279, 1297, 1367, 1447, 1621, 1637, 1693, 1999, 2111, 2161, 2179, 2213, 2269, 2339, 2393, 2663, 2699, 2719, 2791, 2917, 2969, 2971, 3167, 3169, 3221, 3329, 3463, 3499, 3617

Offset: 1

Jaroslav Krizek, Nov 13 2011

Complement of A199981 with respect to A034049, numbers whose multiplicative digital root is 2.

			Prime 389 is in sequence because 3*8*9=216, 2*1*6 =12, 1*2=2.

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

Cf. A199981 (nonprime numbers whose multiplicative digital root is 2).
Includes A107612.
Cf. A031347, A034049.

mdr:= proc(n) option remember;
  local t;
  t:= convert(convert(n,base,10),`*`);
  if t < 10  then t else procname(t) fi
end proc:
select(t -> mdr(t) = 2 and isprime(t), [2, seq(i,i=3..10000,2)]); # Robert Israel, Nov 05 2020

t = {}; n = 0; While[Length[t] < 100, n = NextPrime[n]; s = n; While[s >= 10, s = Times @@ IntegerDigits[s]]; If[s == 2, AppendTo[t, n]]]; t (* T. D. Noe, Nov 15 2011 *)
Select[Prime[Range[600]],FixedPoint[Times@@IntegerDigits[#]&,#]==2&] (* Harvey P. Dale, Mar 28 2012 *)

A201015 Composite numbers whose product of digits is 2.

Original entry on oeis.org

12, 21, 112, 121, 1112, 1121, 1211, 11112, 11121, 11211, 12111, 21111, 111112, 121111, 211111, 1111112, 1111121, 1112111, 1121111, 1211111, 2111111, 11111112, 11111121, 11111211, 11112111, 11121111, 11211111, 12111111, 21111111, 111111112, 111111121, 111111211

Offset: 1

Jaroslav Krizek, Nov 25 2011

Complement of A107612 with respect to A199986. Subsequence of A199981 (composite numbers whose multiplicative digital root is 2).

			Number 121 is in sequence because 1*2*1 = 2, and 121 = 11*11 is composite.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A107612 (primes whose product of digits is 2), A199986 (numbers whose product of digits is 2).

Select[Sort[Flatten[Table[FromDigits/@Permutations[PadRight[{2},n,1]],{n,2,9}]]],CompositeQ] (* Harvey P. Dale, Oct 06 2024 *)

from sympy import isprime
def agen(maxdigits):
    for digs in range(1, maxdigits+1):
        for i in range(digs):
            t = int("1"*(digs-1-i) + "2" + "1"*i)
            if not isprime(t): yield t
print(list(agen(9))) # Michael S. Branicky, Dec 21 2021

cp's OEIS Frontend

A199980 Primes whose multiplicative digital root is 2.

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