This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A267764 #19 Jul 02 2019 02:11:34 %S A267764 0,1,16,25,256,289,400,441,673,1761,1849,4096,4225,4624,4761,6400, %T A267764 6561,7056,7713,10768,13401,28176,29584,65536,66049,67600,68121,73984, %U A267764 74529,76176,76729,77985,102400,103041,104976,112896,113569,123408,150081,172288,214416,450816,473344,501433,519873 %N A267764 Numbers whose base-4 representation is a square when read in base 10. %C A267764 Trivially includes powers of 16, since 16^k = 100..00_4 = 10^(2k) when read as a base-10 number. Moreover, for any a(n) in the sequence, 16*a(n) is also in the sequence. One could call "primitive" the terms not of this form, these would be 1, 25 = 121_4, 289 = 10201_4, 441 = 12321_4, 673 = 22201_4, 1761 = 123201_4, ... These primitive terms include the subsequence 16^k + 2*4^k + 1 = (4^k+1)^2, k > 0, which yields A033934 when written in base 4. %H A267764 Chai Wah Wu, <a href="/A267764/b267764.txt">Table of n, a(n) for n = 1..10000</a> %t A267764 Select[Range[1000], IntegerQ[Sqrt[FromDigits[IntegerDigits[#, 4]]]] &] (* _Alonso del Arte_, Jan 23 2016 *) %o A267764 (PARI) is(n,b=4,c=10)=issquare(subst(Pol(digits(n,b)),x,c)) %o A267764 (Python) %o A267764 A267764_list = [int(d,4) for d in (str(i**2) for i in range(10**6)) if max(d) < '4'] # _Chai Wah Wu_, Feb 23 2016 %Y A267764 Cf. A267763 - A267769 for bases 3 through 9. The base-2 analog is A000302 = powers of 4. %Y A267764 For a "prime" analog see also A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. %K A267764 nonn,base %O A267764 1,3 %A A267764 _M. F. Hasler_, Jan 20 2016