cp's OEIS Frontend

A267766 Numbers whose base-6 representation is a square when read in base 10.

%I A267766 #19 Sep 08 2022 08:46:15
%S A267766 0,1,4,17,36,49,64,89,124,144,169,232,305,388,409,449,544,577,612,665,
%T A267766 953,1105,1296,1369,1444,1529,1764,1849,1936,2033,2304,2825,3097,3204,
%U A267766 3280,3473,4345,4464,4588,4841,5104,5184,5329,5633,6084,6241,7081,7649,8044,8352,8449,9160,9593
%N A267766 Numbers whose base-6 representation is a square when read in base 10.
%C A267766 Trivially includes powers of 36, since 36^k = 100..00_6 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 36*a(n) is also in the sequence. One could call "primitive" the terms not of this form. These primitive terms include the subsequence 36^k + 2*6^k + 1 = (6^k+1)^2, k > 0, which yields A033934 when written in base 6.
%H A267766 Chai Wah Wu, <a href="/A267766/b267766.txt">Table of n, a(n) for n = 1..10000</a>
%t A267766 Select[Range[0, 10^4], IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 6] &] (* _Michael De Vlieger_, Jan 24 2016 *)
%o A267766 (PARI) is(n,b=6,c=10)=issquare(subst(Pol(digits(n,b)),x,c))
%o A267766 (Magma) [n: n in [0..10^4] | IsSquare(Seqint(Intseq(n,6)))]; // _Bruno Berselli_, Jan 20 2016
%o A267766 (Python)
%o A267766 A267766_list = [int(d,6) for d in (str(i**2) for i in range(10**6)) if max(d) < '6'] # _Chai Wah Wu_, Mar 12 2016
%Y A267766 Cf. A267763 - A267769 for bases 3 through 9. The base-2 analog is A000302 = powers of 4.
%Y A267766 For a "prime" analog see also A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924.
%K A267766 nonn,base
%O A267766 1,3
%A A267766 _M. F. Hasler_, Jan 20 2016