A233452 Numbers k such that k^6 starts with k itself (in base 10).
0, 1, 4, 10, 16, 40, 100, 631, 1000, 1585, 2512, 10000, 15849, 25119, 100000, 1000000, 10000000, 15848932, 100000000, 1000000000, 6309573445, 10000000000, 100000000000, 251188643151, 1000000000000, 3981071705535, 6309573444802, 10000000000000
Offset: 1
Examples
4^6 = 4096 begins with 4, so 4 is in the sequence.
Programs
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Mathematica
kmax=10^6; Select[Range[0,kmax],FromDigits[Drop[IntegerDigits[#^6],-(IntegerLength[#^6]-IntegerLength[#])]]==# &] (* Stefano Spezia, Aug 27 2023 *)
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PARI
r=65; print1(1, ", "); e=6; for(n=2, r, p=round((10^(1/(e-1)))^n); f=p^e; b=10^(#Str(f)-#Str(p)); if((f-lift(Mod(f, b)))/b==p, print1(p, ", ")));
Extensions
0 inserted by Juhani Heino, Aug 31 2015