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

1,3

Links

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

Example

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

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 *)

Prog

(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, ", ")));

Crossrefs

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

Sequence in context: A228989 A072083 A029793 * A358442 A136877 A257969

Adjacent sequences: A233450 A233451 A233452 * A233454 A233455 A233456

Keyword

nonn,base,easy

Author

Arkadiusz Wesolowski, Dec 10 2013

Extensions

0 inserted by Juhani Heino, Aug 31 2015

Status

approved