A345875 Numbers whose fourth powers are zeroless pandigital.

608, 809, 897, 924, 1166, 1241, 1458, 1459, 1506, 1547, 1718, 1729, 1832, 1932, 1977, 1982, 2112, 2162, 2179, 2188, 2211, 2279, 2283, 2291, 2296, 2336, 2337, 2408, 2427, 2541, 2592, 2594, 2613, 2634, 2684, 2689, 2704, 2764, 2776, 2779, 2854, 2941, 2984, 2988, 3009

Offset: 1

Author

Tanya Khovanova, Jun 27 2021

Keywords

• nonn
• base

Comments

Zeroless pandigital means that it contains all the digits 1 through 9, but doesn't contain a zero.

Examples

			608^4 = 136651472896. Thus, 608 belongs to this sequence.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071519 (for squares), A124628 (for cubes).

Subsequence of A121321 (4th power is pandigital).

Programs

Maple

q:= n-> is({convert(n^4, base, 10)[]}={$1..9}):
select(q, [$1..3000])[];  # Alois P. Heinz, Jun 29 2021

Mathematica

Select[Range[8000], Union[IntegerDigits[#^4]] == {1, 2, 3, 4, 5, 6, 7, 8, 9} &]

PARI

isok(k) = my(d=digits(k^4)); vecmin(d) && (#Set(d) == 9); \\ Michel Marcus, Jun 30 2021

Python

def ok(n): return set(str(n**4)) == set("123456789")
print(list(filter(ok, range(3000)))) # Michael S. Branicky, Jun 27 2021