cp's OEIS Frontend

A030485 Squares composed of digits {2, 5, 7}.

%I A030485 #39 Oct 18 2024 16:15:23
%S A030485 25,225,7225,27225,55225,2772225,227557225,277722225,27777222225,
%T A030485 72272257225,2777772222225,25772527522225,277777722222225,
%U A030485 2775552752755225,27522257555772225,27777777222222225,77525222275255225,257727727257277225,722555225555275225,2275752775775227225
%N A030485 Squares composed of digits {2, 5, 7}.
%C A030485 We can easily prove that, except for the first term, all terms are of the form 100*m^2 + 100*m + 25 where mod(m, 10) is one of the numbers 1, 3, 6 or 8. Also we can show that all numbers of the form ((5 * 10^n - 5)/3)^2 where n is a natural number, are in the sequence. - _Farideh Firoozbakht_, Dec 09 2008
%H A030485 Zhao Hui Du, <a href="/A030485/b030485.txt">Table of n, a(n) for n = 1..45</a>
%H A030485 Patrick De Geest, <a href="http://www.worldofnumbers.com/threedigits.htm">Squares containing at most three distinct digits, Index entries for related sequences</a>
%F A030485 a(n) = A030487(n)^2. - _M. F. Hasler_, Dec 23 2012
%t A030485 Flatten[Table[Select[FromDigits/@Tuples[{2, 5, 7}, n], IntegerQ[Sqrt[#]] &], {n, 17}]] (* The program takes a long time to run *) (* _Harvey P. Dale_, Jan 18 2015 *)
%t A030485 Select[(5Range[1, 9999, 2])^2, Complement[IntegerDigits[#], {2, 5, 7}] == {} &] (* _Alonso del Arte_, Feb 19 2020 *)
%o A030485 (PARI) fromTernary(n, d)=sum(i=0,d-1,[2,5,7][(n\3^i)%3+1]*10^i)
%o A030485 v=List([25]);for(d=0,16,for(n=0,3^d-1,if(issquare(t=225+1000*fromTernary(n,d)), listput(v,t); print1(t", ")))); Vec(v) \\ _Charles R Greathouse IV_, Dec 22 2012
%Y A030485 Subsequence of A191486. Also subsequence of A017330. Cf. A030487.
%K A030485 nonn,base
%O A030485 1,1
%A A030485 _Patrick De Geest_, Dec 11 1999
%E A030485 Extended and corrected by author, May 08 2000
%E A030485 a(17)-a(19) from _Farideh Firoozbakht_, Dec 09 2008