A233453 Numbers k such that k^7 starts with k itself (in base 10).

0, 1, 10, 100, 1000, 6813, 10000, 14678, 46416, 100000, 146780, 464159, 1000000, 4641589, 10000000, 21544347, 68129207, 100000000, 1000000000, 10000000000, 100000000000, 316227766017, 681292069058, 1000000000000, 2154434690032, 10000000000000, 21544346900319

Offset: 1

Author

Arkadiusz Wesolowski, Dec 10 2013

Keywords

• nonn
• base
• easy

Examples

			6813^7 = 681347587591081074493576917 begins with 6813, so 6813 is in the sequence.
		

Crossrefs

Cf. A052210, A052211, A233451, A233452, A233454, A233455, A233456.

Programs

Mathematica

Join[{0},Select[Range[0,5*10^6],IntegerDigits[#]==Take[IntegerDigits[ #^7],IntegerLength[ #]]&]] (* The program generates the first 14 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Mar 31 2022 *)

PARI

r=80; print1(1, ", "); e=7; 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