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

Author

Jaroslav Krizek, Nov 13 2011

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A199981 (nonprime numbers whose multiplicative digital root is 2).

Includes A107612.

Cf. A031347, A034049.

Programs

Maple

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

Mathematica

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 *)