A034052 Numbers with multiplicative digital root value 5.

5, 15, 35, 51, 53, 57, 75, 115, 135, 151, 153, 157, 175, 315, 351, 355, 359, 395, 511, 513, 517, 531, 535, 539, 553, 557, 571, 575, 579, 593, 597, 715, 751, 755, 759, 795, 935, 953, 957, 975, 1115, 1135, 1151, 1153, 1157, 1175, 1315, 1351, 1355, 1359, 1395

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base
• easy

Comments

All digits of a(n) must be odd. - Robert Israel, Oct 19 2015

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, A371561.

Cf. A034048, A002275, A034049, A034050, A034051, this sequence, 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=5, [$1..10^5]); # Robert Israel, Oct 19 2015

Mathematica

mrQ[n_]:=NestWhile[Times@@IntegerDigits[#]&,n,#>10&]==5; Select[Range[1395],mrQ[#]&] (* Jayanta Basu, May 30 2013 *)

PARI

t(n) = {while(n>9, n=prod(i=1, #n=digits(n), n[i])); n};
for(n=0, 1e4, if(t(n) == 5, print1(n", "))); \\ Altug Alkan, Oct 19 2015

Extensions

Incorrect formula removed by Martin Renner, Oct 19 2015