A373291 Contribution to the OEIS

A373291 This is one of my favorite sequences. Least perfect power of n containing some decimal digit of n. +30 0

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 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 1,2 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 LINKS Table of n, a(n) for n=1..40. FORMULA a(n) = n^A253600(n). EXAMPLE For n=12, 12^2=144 contains digit 1 from n so that a(12) = 144. MATHEMATICA seq={}; Do[k=1; Until[ ContainsAny[IntegerDigits[n], IntegerDigits[n^k] ], k++ ]; AppendTo[seq, n^k] , {n, 40}]; seq PROG (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 CROSSREFS Cf. A111442, A253600. KEYWORD nonn,base,new AUTHOR James C. McMahon, May 30 2024 STATUS approved