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%I #23 Aug 27 2023 16:23:56
%S 0,1,10,100,1000,6813,10000,14678,46416,100000,146780,464159,1000000,
%T 4641589,10000000,21544347,68129207,100000000,1000000000,10000000000,
%U 100000000000,316227766017,681292069058,1000000000000,2154434690032,10000000000000,21544346900319
%N Numbers k such that k^7 starts with k itself (in base 10).
%e 6813^7 = 681347587591081074493576917 begins with 6813, so 6813 is in the sequence.
%t 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 *)
%o (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, ", ")));
%Y Cf. A052210, A052211, A233451, A233452, A233454, A233455, A233456.
%K nonn,base,easy
%O 1,3
%A _Arkadiusz Wesolowski_, Dec 10 2013
%E 0 inserted by _Juhani Heino_, Aug 31 2015