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%I #18 Jul 02 2019 02:11:02
%S 0,1,4,15,23,33,58,73,81,100,121,185,213,265,298,324,361,400,474,509,
%T 555,643,685,751,861,914,1093,1153,1215,1288,1354,1481,1554,1705,1783,
%U 1863,1945,2029,2210,2301,2488,2584,2673,2773,2875,3101,3210,3424,3538,3682,3802,4038,4154,4281,4450
%N Numbers whose base-9 representation is a square when read in base 10.
%C Trivially includes powers of 81, since 81^k = 100..00_9 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 81*a(n) is also in the sequence. One could call "primitive" the terms not of this form. These primitive terms include the subsequence 81^k + 2*9^k + 1 = (9^k+1)^2, k > 0, which yields A033934 when written in base 9.
%H Chai Wah Wu, <a href="/A267769/b267769.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[0, 5000], IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 9] &] (* _Michael De Vlieger_, Jan 24 2016 *)
%o (PARI) is(n,b=9,c=10)=issquare(subst(Pol(digits(n,b)),x,c))
%o (Python)
%o A267769_list = [int(s, 9) for s in (str(i**2) for i in range(10**6)) if max(s) < '9'] # _Chai Wah Wu_, Jan 20 2016
%Y Cf. A267763 - A267768 for bases 3 through 8. 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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