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A273382
Numbers x = concat(a,b) such that a^b begins with the digits of x.
3
7525, 7533, 251196, 264770, 304732, 1768696, 2605292, 2653884, 32554685, 46415894
OFFSET
1,1
EXAMPLE
7525 is a member because 75^25 is equal to 752543...6875, i.e., its first digits are 7525.
MATHEMATICA
beg[x_, y_, n_] := x > 0 && Log10[x]*y >= Log10[n] && Block[{u = FractionalPart@ Log10[n+1]}, FractionalPart@ Log10[n] <= FractionalPart[ Log10[x]*y] < If[u == 0, 1, u]]; ok[n_] := Block[{p=1}, While[(p *= 10) < n && ! beg[Floor[n/p], Mod[n, p], n]]; p < n]; Select[Range[10^6], ok]
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Giovanni Resta, Jun 06 2016
STATUS
approved