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

1,3

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

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

Prog

(Python 3.7)
def getBaseTen(howMany=100):
    listToReturn = []
    listOfObtainedValues = []
    count = 0
    while len(listToReturn) < howMany:
        afterOnePermutation = 1
        for num in str(count):
            afterOnePermutation *= int(num)
            if afterOnePermutation is 0:
                break
        if not afterOnePermutation in listOfObtainedValues:
            listToReturn.append(str(count))
            listOfObtainedValues.append(afterOnePermutation)
        count += 1
    return listToReturn
(PARI) See Links section.

Crossrefs

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

Sequence in context: A069716 A095289 A174141 * A095706 A280249 A096867

Adjacent sequences: A343400 A343401 A343402 * A343404 A343405 A343406

Keyword

nonn,base

Author

Collin King, Apr 14 2021

Status

approved