login
A353057
Numbers N of the form m^k in ascending order having the property that for any choice of m and k such that N = m^k, the sets of distinct digits of m, k, and m^k are pairwise disjoint.
0
8, 9, 16, 49, 81, 1089, 1156, 1444, 1936, 3364, 3481, 4489, 7056, 7744, 8836, 10648, 34969, 35344, 37636, 97969, 98596, 110592, 110889, 111556, 140608, 150544, 190969, 197136, 199809, 306916, 311364, 407044, 444889, 473344, 499849, 544644, 553536, 558009, 561001
OFFSET
1,1
COMMENTS
In this sequence, no similar digit sharing constraint applies between equivalent m^k's, so 2^4 = 4^2 = 16 is a valid term here.
Can a term exist in this sequence where neither m, k, m^k contains the decimal digit 2 in any of the ways m^k may be written? Examples for all the other missing decimal digits from m, k and m^k are easily found among the terms.
EXAMPLE
10648 (where m=22, k=3) is a term because 22^3 = 10648 and the three sets of digits [2], [3] and [1,0,6,4,8] are mutually disjoint.
81 is a term because 3^4 = 81 and the three sets of digits [3], [4] and [8,1] are mutually disjoint. 9^2 = 81 too, and here the three sets of digits [9], [2] and [8,1] are also mutually disjoint. This example illustrates the cases where there is more than one choice for m and k.
CROSSREFS
Cf. A001597.
Sequence in context: A227647 A175053 A350075 * A274406 A261454 A022098
KEYWORD
nonn,base
AUTHOR
Tamas Sandor Nagy, Apr 20 2022
STATUS
approved