login
A233452
Numbers k such that k^6 starts with k itself (in base 10).
7
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
1,3
EXAMPLE
4^6 = 4096 begins with 4, so 4 is in the sequence.
MATHEMATICA
kmax=10^6; Select[Range[0, kmax], FromDigits[Drop[IntegerDigits[#^6], -(IntegerLength[#^6]-IntegerLength[#])]]==# &] (* Stefano Spezia, Aug 27 2023 *)
PROG
(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, ", ")));
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
0 inserted by Juhani Heino, Aug 31 2015
STATUS
approved