A373203 Contribution to the OEIS

 

A373203 a(n) = minimum k>1 such that n^k contains all distinct decimal digits of n. 0

2, 2, 5, 5, 3, 2, 2, 5, 5, 3, 2, 2, 3, 5, 4, 6, 5, 5, 5, 7, 5, 3, 4, 7, 3, 2, 8, 2, 5, 3, 5, 4, 3, 3, 3, 6, 6, 5, 4, 3, 3, 6, 7, 4, 3, 4, 4, 4, 4, 3, 2, 3, 7, 5, 3, 2, 3, 5, 5, 3, 2, 3, 5, 2, 2, 3, 2, 3, 4, 5, 5, 3, 3, 3, 2, 3, 2, 5, 5, 5, 5 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 0,1 LINKS Table of n, a(n) for n=0..80. FORMULA A253600(n) <= a(n) <= A045537(n). - Michael S. Branicky, May 28 2024 A111442(n) = n^a(n). EXAMPLE For n=12, a(12)=3 because 12^3=1728 contains all decimal digits of n. Compare to A253600(12)=2 because 12^2=144 contains any digit of n. MATHEMATICA seq={}; Do[k=1; Until[ContainsAll[IntegerDigits[n^k], IntegerDigits[n] ], k++]; AppendTo[seq, k] , {n, 0, 80}]; seq PROG (Python) from itertools import count def a(n): s = set(str(n)) return next(k for k in count(2) if s <= set(str(n**k))) print([a(n) for n in range(81)]) # Michael S. Branicky, May 27 2024 CROSSREFS Cf. A045537, A111442, A253600. Sequence in context: A005177 A357123 A253600 * A045537 A243941 A161622 Adjacent sequences: A373188 A373189 A373195 * A373207 A373208 A373210 KEYWORD nonn,base,new AUTHOR James C. McMahon, May 27 2024 STATUS approved