A034049 Numbers with multiplicative digital root value 2.

2, 12, 21, 26, 34, 37, 43, 62, 73, 112, 121, 126, 134, 137, 143, 162, 173, 211, 216, 223, 232, 261, 278, 279, 287, 297, 299, 314, 317, 322, 341, 367, 369, 371, 376, 389, 396, 398, 413, 431, 447, 469, 474, 496, 612, 621, 637, 639, 649, 666, 673, 693, 694, 713

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Multiplicative Digital Root
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A031347.

Cf. A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 0-9).

Programs

Maple

A031347:= proc(n) local x;
  x:= n;
  while x > 10 do
    x:= convert(convert(x,base,10),`*`)
  od;
  x
end proc:
select(A031347=2, [$1..1000]); # Robert Israel, Jan 23 2023

Mathematica

t = {}; n = 0; While[Length[t] < 100, n++; s = n; While[s > 10, s = Times @@ IntegerDigits[s]]; If[s == 2, AppendTo[t, n]]]; t (* T. D. Noe, Nov 15 2011 *)

PARI

t(n) = {while(n>9, n=prod(i=1, #n=digits(n), n[i])); n};
for(n=0, 1e3, if(t(n) == 2, print1(n", "))); \\ Altug Alkan, Oct 19 2015

Extensions

Incorrect formula removed by Martin Renner, Oct 19 2015