A034051 Numbers with multiplicative digital root value 4.

4, 14, 22, 27, 39, 41, 72, 89, 93, 98, 114, 122, 127, 139, 141, 172, 189, 193, 198, 212, 217, 221, 249, 266, 271, 277, 294, 319, 333, 338, 346, 364, 379, 383, 391, 397, 411, 429, 436, 463, 492, 626, 634, 643, 662, 677, 712, 721, 727, 739, 767, 772, 776, 793

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..5000
• 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

mdr:= proc(n) option remember;
if n < 10 then return(n) fi;
procname(convert(convert(n,base,10),`*`))
end proc:
select(mdr=4, [$1..10^5]); # Robert Israel, Oct 19 2015

Mathematica

Select[Range@ 800, FixedPoint[Times @@ IntegerDigits@ # &, #] == 4 &] (* Michael De Vlieger, Oct 19 2015 *)

PARI

t(n) = {while(n>9, n=prod(i=1, #n=digits(n), n[i])); n};
for(n=0, 1e4, if(t(n) == 4, print1(n", "))); \\ Altug Alkan, Oct 19 2015

Extensions

Incorrect formula removed by Martin Renner, Oct 19 2015