A233455 Numbers k such that k^9 starts with k itself (in base 10).
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
Examples
750^9 = 75084686279296875000000000 begins with 750, so 750 is in the sequence.
Links
- G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 7499
Programs
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Mathematica
Join[{0}, Select[Range@ 1000000, Take[IntegerDigits[#^9], IntegerLength@ #] == IntegerDigits@ # &]] (* Michael De Vlieger, Aug 31 2015 *) -
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, ", ")));
Extensions
0 inserted by Juhani Heino, Aug 31 2015