A233454 Numbers k such that k^8 starts with k itself (in base 10).

0, 1, 2, 10, 14, 72, 100, 139, 518, 1000, 10000, 13895, 19307, 26827, 37276, 100000, 1000000, 10000000, 13894955, 26826958, 100000000, 193069773, 517947468, 1000000000, 1930697729, 10000000000, 100000000000, 268269579528, 1000000000000, 3727593720315

Offset: 1

Author

Arkadiusz Wesolowski, Dec 10 2013

Keywords

• nonn
• base
• easy

Examples

			2^8 = 256 begins with 2, so 2 is in the sequence.
		

Crossrefs

Cf. A052210, A052211, A233451, A233452, A233453, A233455, A233456.

Programs

Mathematica

Join[{0}, Select[Range@ 1000000, Take[IntegerDigits[#^8], IntegerLength@ #] == IntegerDigits@ # &]] (* Michael De Vlieger, Aug 31 2015 *)

PARI

r=88; print1(1, ", "); e=8; 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