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%I #36 Sep 08 2022 08:45:57
%S 25,225,7225,27225,55225,235225,2772225,3553225,23377225,33235225,
%T 57532225,227557225,252333225,277722225,337273225,357777225,523723225,
%U 735223225,777573225,2523555225,3325252225,3377353225,5232352225,7333353225
%N Squares using only the prime digits (2,3,5,7).
%C a(n) = 225 mod 1000 for n > 1. - _Charles R Greathouse IV_, May 14 2013
%C The sequence is infinite: it contains A030485 as an infinite proper subsequence which in turn contains all numbers of the form ((5*10^n-5)/3)^2 as a proper subsequence. - _M. F. Hasler_, Sep 16 2016
%H Charles R Greathouse IV and Donovan Johnson, <a href="/A191486/b191486.txt">Table of n, a(n) for n = 1..1000</a> (first 155 terms from Charles R Greathouse IV)
%F a(n) = A275971(n)^2. - _M. F. Hasler_, Sep 16 2016
%p for b from 1 do convert(convert(b^2,base,10),set) ; if % minus {2,3,5,7} = {} then printf("%d,\n",b^2) ; end if; end do: # _R. J. Mathar_, Jun 03 2011
%t w = Boole@! PrimeQ@ # & /@ RotateLeft@ Range[0, 9]; Select[Range[10^5]^2, Total@ Pick[DigitCount@ #, w, 1] == 0 &] (* _Michael De Vlieger_, Aug 15 2016 *)
%o (Magma) [n^2: n in [5..5*10^5] | Set(Intseq(n^2)) subset {2,3,5,7}]; // _Bruno Berselli_, Jun 06 2011
%o (PARI) toprime(n,k)=n<<=2;sum(i=0,k-1,n>>=2;[2,3,5,7][bitand(n,3)+1]*10^i)
%o v=List([25]);for(k=0,9,for(n=0,4^k-1,t=1000*toprime(n,k)+225;if(issquare(t),listput(v,t)))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, May 14 2013
%o (Python)
%o from math import isqrt
%o def aupto(limit):
%o alst, rootlimit = [], isqrt(limit)
%o for k in range(1, rootlimit+1):
%o if set(str(k*k)) <= set("2357"): alst.append(k*k)
%o return alst
%o print(aupto(7333353225)) # _Michael S. Branicky_, May 15 2021
%Y Cf. A077676, A030485.
%K nonn,base
%O 1,1
%A _Giovanni Teofilatto_, Jun 03 2011
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