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A273382 Numbers x = concat(a,b) such that a^b begins with the digits of x. 3

%I #8 Jun 06 2016 08:10:28

%S 7525,7533,251196,264770,304732,1768696,2605292,2653884,32554685,

%T 46415894

%N Numbers x = concat(a,b) such that a^b begins with the digits of x.

%e 7525 is a member because 75^25 is equal to 752543...6875, i.e., its first digits are 7525.

%t 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]

%Y Cf. A266817, A266818, A273383.

%K nonn,base,more

%O 1,1

%A _Giovanni Resta_, Jun 06 2016

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Last modified February 28 19:33 EST 2024. Contains 370400 sequences. (Running on oeis4.)