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

25, 225, 7225, 27225, 55225, 2772225, 227557225, 277722225, 27777222225, 72272257225, 2777772222225, 25772527522225, 277777722222225, 2775552752755225, 27522257555772225, 27777777222222225, 77525222275255225, 257727727257277225, 722555225555275225, 2275752775775227225

Offset: 1

Author

Patrick De Geest, Dec 11 1999

Keywords

• nonn
• base

Comments

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

Links

• Zhao Hui Du, Table of n, a(n) for n = 1..45
• Patrick De Geest, Squares containing at most three distinct digits, Index entries for related sequences

Crossrefs

Subsequence of A191486. Also subsequence of A017330. Cf. A030487.

Programs

Mathematica

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 *)
Select[(5Range[1, 9999, 2])^2, Complement[IntegerDigits[#], {2, 5, 7}] == {} &] (* Alonso del Arte, Feb 19 2020 *)

PARI

fromTernary(n, d)=sum(i=0,d-1,[2,5,7][(n\3^i)%3+1]*10^i)
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

Formula

a(n) = A030487(n)^2. - M. F. Hasler, Dec 23 2012

Extensions

Extended and corrected by author, May 08 2000

a(17)-a(19) from Farideh Firoozbakht, Dec 09 2008