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

1,3

Links

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

Example

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

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 *)

Prog

(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, ", ")));

Crossrefs

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

Sequence in context: A198309 A167342 A288781 * A177172 A358985 A171767

Adjacent sequences: A233448 A233449 A233450 * A233452 A233453 A233454

Keyword

nonn,base,easy

Author

Arkadiusz Wesolowski, Dec 10 2013

Extensions

0 inserted by Juhani Heino, Aug 31 2015

Status

approved