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A233455
Numbers k such that k^9 starts with k itself (in base 10).
7
0, 1, 10, 75, 100, 750, 1000, 4217, 7499, 10000, 100000, 177828, 1000000, 10000000, 74989421, 100000000, 1000000000, 5623413252, 10000000000, 100000000000, 177827941004, 1000000000000, 1778279410039, 10000000000000, 56234132519035, 100000000000000
OFFSET
1,3
LINKS
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 7499
EXAMPLE
750^9 = 75084686279296875000000000 begins with 750, so 750 is in the sequence.
MATHEMATICA
Join[{0}, Select[Range@ 1000000, Take[IntegerDigits[#^9], IntegerLength@ #] == IntegerDigits@ # &]] (* Michael De Vlieger, Aug 31 2015 *)
PROG
(PARI) r=112; print1(1, ", "); e=9; 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