A343403 Numbers k such that the product of the digits of k is not the product of digits of any earlier term in the sequence.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 25, 26, 27, 28, 29, 35, 37, 38, 39, 45, 47, 48, 49, 55, 56, 57, 58, 59, 67, 68, 69, 77, 78, 79, 88, 89, 99, 255, 256, 257, 258, 259, 267, 268, 269, 277, 278, 279, 288, 289, 299, 355, 357, 358, 359, 377, 378, 379, 388, 389, 399, 455

Offset: 1

Author

Collin King, Apr 14 2021

Keywords

• nonn
• base

Comments

Observations:

The digits 0 and 1 appear only in terms 0 and 1, respectively.

Terms cannot contain two 2s, two 3s, a 2 and a 3, a 2 and a 4, a 3 and a 4, or a 4 and a 6.

Digits in each term appear in ascending order (A009994).

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A343403

Crossrefs

Cf. A003001, A007954, A009994 (ascending digits), A031346, A068189, A343160.

Programs

Maple

# product of digits
A007954 := proc(n::integer)
    if n = 0 then
        0;
    else
        mul( d, d=convert(n, base, 10)) ;
    end if;
end proc:
hit:=Array(0..10000,-1);
a:=[0];
hit[0]:=0;
for n from 1 to 50000 do p:=A007954(n);
   if p>0 and hit[p]=-1 then hit[p]:=n; a:=[op(a),n]; fi; od:
a; # N. J. A. Sloane, Apr 14 2021

PARI

See Links section.