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%I #18 Sep 08 2022 08:46:15
%S 0,1,9,16,81,100,144,235,729,784,900,961,1296,1369,2115,6561,6724,
%T 7056,7225,8100,8649,11664,11881,12321,15985,19035,59049,59536,60516,
%U 61009,63504,64009,65025,72900,73441,77841,104976,105625,106929,110889,143865,171315,182428,531441,532900,535824,537289,544644,546121
%N Numbers whose base-3 representation is a square when read in base 10.
%C Trivially includes powers of 9, since 9^k = 100..00_3 = 10^(2k) when read as a base-10 number. Moreover, for any a(n) in the sequence, 9*a(n) is also in the sequence. One could call "primitive" the terms not of this form; these would be 1, 16 = 121_3, 100 = 10201_3, 235 = 22201_3, 784 = 1002001_3, 961 = 1022121_3, ... These primitive terms include the subsequence 9^k + 2*3^k + 1, k > 0, which yields A033934 when written in base 3.
%H Chai Wah Wu, <a href="/A267763/b267763.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[0, 600000], IntegerQ@Sqrt@FromDigits@IntegerDigits[#, 3] &] (* _Vincenzo Librandi_ Dec 28 2016 *)
%o (PARI) is(n,b=3,c=10)=issquare(subst(Pol(digits(n,b)),x,c))
%o (Python)
%o A267763_list = [int(d,3) for d in (str(i**2) for i in range(10**6)) if max(d) < '3'] # _Chai Wah Wu_, Mar 12 2016
%o (Magma) [n: n in [0..10^6] | IsSquare(Seqint(Intseq(n, 3)))]; // _Vincenzo Librandi_, Dec 28 2016
%Y Cf. A267764 - A267769 for bases 4 through 9. The base-2 analog is A000302 = powers of 4.
%Y For a "prime" analog see also A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924.
%K nonn,base
%O 1,3
%A _M. F. Hasler_, Jan 20 2016
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