cp's OEIS Frontend

A256523 Numbers m such that m, m^2 and m^3 have identical initial digits in decimal representation.

%I A256523 #13 Dec 17 2024 18:29:58
%S A256523 0,1,10,11,12,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
%T A256523 111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,966,967,
%U A256523 968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985
%N A256523 Numbers m such that m, m^2 and m^3 have identical initial digits in decimal representation.
%C A256523 Intersection of A089951 and A144582.
%C A256523 From _Jianing Song_, Dec 26 2022: (Start)
%C A256523 For k > 0, write k = s * 10^t, 1 <= s < 10, then k is a term if and only if s is in [1, 2^(1/3)) U (30^(2/3), 10).
%C A256523 Except for 0, terms of A144582 that start with 1 or 9. (End)
%H A256523 Reinhard Zumkeller, <a href="/A256523/b256523.txt">Table of n, a(n) for n = 1..10000</a>
%F A256523 A000030(a(n)) = A002993(a(n)) = A000030(A000290(a(n))) = A002994(a(n)) = A000030(A000578(a(n))).
%t A256523 Select[Range[0,1000],Length[Union[(IntegerDigits/@(#^Range[3]))[[;;,1]]]]==1&] (* _Harvey P. Dale_, Dec 17 2024 *)
%o A256523 (Haskell)
%o A256523 a256523 n = a256523_list !! (n-1)
%o A256523 a256523_list = [x | x <- [0..], let i = a000030 x,
%o A256523                     a000030 (x ^ 2) == i, a000030 (x ^ 3) == i]
%o A256523 (PARI) initial(n)=digits(n)[1]
%o A256523 is(n)=if(n==0, return(1)); my(k=initial(n)); initial(n^2)==k && initial(n^3)==k \\ _Charles R Greathouse IV_, May 13 2015
%Y A256523 Cf. A000030, A089951, A144582, A000290, A000578, A002993, A002994.
%K A256523 nonn,base
%O A256523 1,3
%A A256523 _Reinhard Zumkeller_, Apr 01 2015