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Numbers whose fourth powers are zeroless pandigital.
1

%I #18 Jan 10 2023 20:30:05

%S 608,809,897,924,1166,1241,1458,1459,1506,1547,1718,1729,1832,1932,

%T 1977,1982,2112,2162,2179,2188,2211,2279,2283,2291,2296,2336,2337,

%U 2408,2427,2541,2592,2594,2613,2634,2684,2689,2704,2764,2776,2779,2854,2941,2984,2988,3009

%N Numbers whose fourth powers are zeroless pandigital.

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

%H Alois P. Heinz, <a href="/A345875/b345875.txt">Table of n, a(n) for n = 1..10000</a>

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

%p q:= n-> is({convert(n^4, base, 10)[]}={$1..9}):

%p select(q, [$1..3000])[]; # _Alois P. Heinz_, Jun 29 2021

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

%o (Python)

%o def ok(n): return set(str(n**4)) == set("123456789")

%o print(list(filter(ok, range(3000)))) # _Michael S. Branicky_, Jun 27 2021

%o (PARI) isok(k) = my(d=digits(k^4)); vecmin(d) && (#Set(d) == 9); \\ _Michel Marcus_, Jun 30 2021

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

%Y Subsequence of A121321 (4th power is pandigital).

%K nonn,base

%O 1,1

%A _Tanya Khovanova_, Jun 27 2021