A373291 - OEIS

%I #10 May 31 2024 14:13:23

%S 1,32,243,64,25,36,16807,32768,729,100,121,144,169,196,225,256,4913,

%T 5832,361,400,441,234256,529,13824,625,676,729,784,24389,900,961,1024,

%U 35937,39304,1225,1296,1369,54872,59319,1600

%N Least perfect power of n containing some decimal digit of n.

%C "Perfect power of n" here means n^k with k>1. The sequence gives the value of n^k, not the value of k. - _N. J. A. Sloane_, May 31 2024

%F a(n) = n^A253600(n).

%e For n=12, 12^2=144 contains digit 1 from n so that a(12) = 144.

%t seq={}; Do[k=1;  Until[  ContainsAny[IntegerDigits[n],IntegerDigits[n^k] ],k++  ];AppendTo[seq,n^k] ,{n,40}];seq

%o (PARI) a(n) = my(sd = Set(vecsort(digits(n))), k=2); while (#setintersect(sd, Set(vecsort(digits(n^k)))) == 0, k++); n^k; \\ _Michel Marcus_, May 31 2024

%Y Cf. A111442, A253600.

%K nonn,base

%O 1,2

%A _James C. McMahon_, May 30 2024