A346135 Numbers k such that k and 4k, taken together, contain all digits 1 though 9 at least once.

3942, 4392, 5796, 7956, 11738, 11963, 13196, 13692, 13698, 13724, 13742, 13942, 14237, 14392, 14673, 14693, 15473, 15737, 15873, 15942, 15948, 16473, 17357, 17358, 17381, 17438, 17453, 17458, 17463, 18559, 18592, 19463, 19613, 19631, 19643, 19863, 21369, 21374, 21394, 21439

Offset

1,1

Comments

The first four members use all the digits 1-9 exactly once. They form the sequence A115929.

Links

Table of n, a(n) for n=1..40.

Example

3942 and 3942*4=15768 use once all the digits from 1 to 9.
11738 and 11738*4=46952 use all the digits from 1 to 9 with repetitions.

Maple

q:= n-> (s-> is({seq(parse(s[i]), i=1..length(s))}={$1..9}))(cat("", n, 4*n)):
select(q, [$1..22000])[];  # Alois P. Heinz, Jul 05 2021

Mathematica

Select[Range[1000, 99999], Union[IntegerDigits[#], IntegerDigits[4 #]] == {1, 2, 3, 4, 5, 6, 7, 8, 9} &]

Prog

(Python)
def ok(n): return (set(str(n)) | set(str(4*n))) == set("123456789")
print(list(filter(ok, range(21440)))) # Michael S. Branicky, Jul 05 2021
(PARI) isok(k) = my(s=setunion(Set(digits(k)), Set(digits(4*k)))); vecmin(s) && (#s == 9); \\ Michel Marcus, Jul 11 2021

Crossrefs

Cf. A115929 (finite subsequence).

Sequence in context: A233688 A162859 A115929 * A070185 A059354 A059666

Adjacent sequences: A346132 A346133 A346134 * A346136 A346137 A346138

Keyword

nonn,base

Author

Tanya Khovanova, Jul 05 2021

Status

approved