A199977 Primes whose multiplicative digital root is 0.

59, 101, 103, 107, 109, 239, 251, 257, 269, 293, 307, 349, 353, 401, 409, 439, 457, 479, 503, 509, 521, 523, 541, 547, 563, 569, 577, 587, 599, 601, 607, 619, 653, 659, 691, 701, 709, 757, 787, 809, 853, 857, 859, 877, 907, 947, 997, 1009, 1013, 1019, 1021

Offset: 1

Author

Jaroslav Krizek, Nov 13 2011

Keywords

• nonn
• base

Comments

Complement of A199978 with respect to A034048.

Examples

			Prime 239 is in sequence because 2*3*9 = 45, 4*5 = 20, 2*0 = 0.
		

Links

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

Crossrefs

Cf. A199978 (nonprime numbers whose multiplicative digital root is 0).

Programs

Maple

mdr:= proc(n) local L,r;
  r:= n;
  while r >= 10 do
    r:= convert(convert(r,base,10),`*`)
  od;
  r
end proc:
select(mdr=0, [seq(ithprime(i),i=1..1000)]); # Robert Israel, Feb 28 2021

Mathematica

digRoot[n_] := Module[{k = n}, While[k > 9, k = Times @@ IntegerDigits[k]]; k]; Select[Range[1200], PrimeQ[#] && digRoot[#] == 0 &] (* T. D. Noe, Nov 23 2011 *)