A233451 Numbers k such that k^5 starts with k itself (in base 10).

0, 1, 10, 18, 100, 178, 1000, 10000, 17783, 31623, 100000, 177828, 316228, 1000000, 10000000, 100000000, 1000000000, 5623413252, 10000000000, 100000000000, 177827941004, 316227766017, 1000000000000, 1778279410039, 10000000000000, 31622776601684

Offset: 1

Author

Arkadiusz Wesolowski, Dec 10 2013

Keywords

• nonn
• base
• easy

Examples

			18^5 = 1889568 begins with 18, so 18 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1756

Crossrefs

Cf. A052210, A052211, A233452, A233453, A233454, A233455, A233456.

Programs

Maple

R:= 0,1:
for d from 1 to 100 do
  k:= ceil(10^(d/4));
  if k^5 - 10^d * k < 10^d then
    R:= R, k
  fi
od:
R; # Robert Israel, Sep 11 2024

Mathematica

kmax=10^6; Select[Range[0,kmax],FromDigits[Drop[IntegerDigits[#^5],-(IntegerLength[#^5]-IntegerLength[#])]]==# &] (* Stefano Spezia, Aug 27 2023 *)

PARI

r=54; print1(1, ", "); e=5; 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