A233456 Numbers k such that k^10 starts with k itself (in base 10).

0, 1, 6, 10, 13, 36, 60, 100, 1000, 10000, 100000, 129155, 278256, 1000000, 10000000, 21544347, 100000000, 1000000000, 10000000000, 59948425032, 100000000000, 599484250319, 1000000000000, 10000000000000, 100000000000000, 464158883361278, 1000000000000000

Offset

1,3

Links

Table of n, a(n) for n=1..27.

Example

6^10 = 60466176 begins with 6, so 6 is in the sequence.

Mathematica

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

Prog

(PARI) r=135; print1(1, ", "); e=10; 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, A233452, A233453, A233454, A233455.

Sequence in context: A315156 A315157 A135596 * A189762 A163814 A088706

Adjacent sequences: A233453 A233454 A233455 * A233457 A233458 A233459

Keyword

nonn,base,easy

Author

Arkadiusz Wesolowski, Dec 10 2013

Extensions

0 inserted by Juhani Heino, Aug 31 2015

Status

approved