cp's OEIS Frontend

A267768 Numbers whose base-8 representation is a square when read in base 10.

%I A267768 #16 Sep 08 2022 08:46:15
%S A267768 0,1,4,14,21,30,52,64,81,100,149,174,212,241,256,289,382,405,446,532,
%T A267768 622,661,804,849,896,1012,1045,1102,1220,1281,1344,1409,1476,1557,
%U A267768 1630,1780,1920,2001,2197,2286,2452,2545,2593,2878,2965,3070,3233,3328,3441,3540,3630,3733,4068,4096
%N A267768 Numbers whose base-8 representation is a square when read in base 10.
%C A267768 Trivially includes powers of 64, since 64^k = 100..00_8 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 64*a(n) is also in the sequence. One could call "primitive" the terms not of this form. These primitive terms include the subsequence 64^k + 2*8^k + 1 = (8^k+1)^2, k > 0, which yields A033934 when written in base 8.
%C A267768 Motivated by the subsequence A267490 which lists the primes in this sequence.
%H A267768 Chai Wah Wu, <a href="/A267768/b267768.txt">Table of n, a(n) for n = 1..10000</a>
%t A267768 Select[Range[0, 2 10^4], IntegerQ@Sqrt@FromDigits@IntegerDigits[#, 8] &] (* _Vincenzo Librandi_, Dec 28 2016 *)
%o A267768 (PARI) is(n,b=8,c=10)=issquare(subst(Pol(digits(n,b)),x,c))
%o A267768 (Python)
%o A267768 A267768_list = [int(s, 8) for s in (str(i**2) for i in range(10**6)) if max(s) < '8'] # _Chai Wah Wu_, Jan 20 2016
%o A267768 (Magma) [n: n in [0..10^4] | IsSquare(Seqint(Intseq(n, 8)))]; // _Vincenzo Librandi_, Dec 28 2016
%Y A267768 Cf. A267763 - A267769 for bases 3 through 9. The base-2 analog is A000302 = powers of 4.
%Y A267768 For a "prime" analog see also A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924.
%K A267768 nonn,base
%O A267768 1,3
%A A267768 _M. F. Hasler_, Jan 20 2016