login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%I #22 Aug 27 2023 16:40:02

%S 0,1,6,10,13,36,60,100,1000,10000,100000,129155,278256,1000000,

%T 10000000,21544347,100000000,1000000000,10000000000,59948425032,

%U 100000000000,599484250319,1000000000000,10000000000000,100000000000000,464158883361278,1000000000000000

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

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

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

%o (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, ", ")));

%Y Cf. A052210, A052211, A233451, A233452, A233453, A233454, A233455.

%K nonn,base,easy

%O 1,3

%A _Arkadiusz Wesolowski_, Dec 10 2013

%E 0 inserted by _Juhani Heino_, Aug 31 2015