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

1,1

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.

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 *)

Prog

(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

Crossrefs

Cf. A031347.

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

Sequence in context: A369303 A031001 A048955 * A271361 A304813 A279424

Adjacent sequences: A034046 A034047 A034048 * A034050 A034051 A034052

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Extensions

Incorrect formula removed by Martin Renner, Oct 19 2015

Status

approved