A373291 Least perfect power of n containing some decimal digit of n.

1, 32, 243, 64, 25, 36, 16807, 32768, 729, 100, 121, 144, 169, 196, 225, 256, 4913, 5832, 361, 400, 441, 234256, 529, 13824, 625, 676, 729, 784, 24389, 900, 961, 1024, 35937, 39304, 1225, 1296, 1369, 54872, 59319, 1600

Offset: 1

Author

James C. McMahon, May 30 2024

Keywords

• nonn
• base

Comments

"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

Examples

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

Crossrefs

Cf. A111442, A253600.

Programs

Mathematica

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

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

Formula

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