A371469 - OEIS

%I #23 Jun 12 2024 17:39:41

%S 1023456789,3175462089,4680215379,5702631489,7351062489,7025869314

%N Least pandigital number whose n-th power contains each digit (0-9) exactly n times.

%C If an n-th power of a pandigital number k contains each digit (0-9) exactly n times, it implies that 10^(10 - 1/n) <= 9876543210, so n <= 185. It's easy to verify that no solutions exist for n=7 to 185.

%C For the largest pandigital number whose n-th power contains each digit (0-9) exactly n times, see A370667.

%e a(4) = 5702631489 because it is the least 10-digit number that contains each digit (0-9) exactly once and its 4th power 1057550783692741389295697108242363408641 contains each digit (0-9) exactly 4 times.

%t s = FromDigits /@ Permutations[Range[0, 9]]; For[n = 1, n < 7, n++,

%t  For[k = 1, k <= Length@s, k++,

%t   If[Count[Tally[IntegerDigits[s[[k]]^n]][[All, 2]], n] == 10,

%t    Print[{n, s[[k]]}]; Break[]]]]

%o (Python)

%o from itertools import permutations as per

%o a=[]

%o for n in range(1,7):

%o     for k in [int(''.join(d)) for d in per('0123456789', 10)]:

%o         if all(str(k**n).count(d) ==n for d in '0123456789'):

%o             a.append(k)

%o             break

%o print(a)

%Y Cf. A050278, A199630, A199631, A199632, A199633, A078255, A154532, A154566, A357755, A365144, A370667.

%K base,easy,fini,full,nonn,less

%O 1,1

%A _Zhining Yang_, Apr 01 2024