A233452 Numbers k such that k^6 starts with k itself (in base 10).

0, 1, 4, 10, 16, 40, 100, 631, 1000, 1585, 2512, 10000, 15849, 25119, 100000, 1000000, 10000000, 15848932, 100000000, 1000000000, 6309573445, 10000000000, 100000000000, 251188643151, 1000000000000, 3981071705535, 6309573444802, 10000000000000

Offset

1,3

Links

Table of n, a(n) for n=1..28.

Example

4^6 = 4096 begins with 4, so 4 is in the sequence.

Mathematica

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

Prog

(PARI) r=65; print1(1, ", "); e=6; 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, A233451, A233453, A233454, A233455, A233456.

Sequence in context: A172126 A025621 A056486 * A061682 A246882 A038240

Adjacent sequences: A233449 A233450 A233451 * A233453 A233454 A233455

Keyword

nonn,base,easy

Author

Arkadiusz Wesolowski, Dec 10 2013

Extensions

0 inserted by Juhani Heino, Aug 31 2015

Status

approved