cp's OEIS Frontend

A267767 Numbers whose base-7 representation is a square when read in base 10.

%I A267767 #16 Sep 08 2022 08:46:15
%S A267767 0,1,4,13,19,27,46,49,64,81,117,139,165,190,196,225,313,361,433,460,
%T A267767 571,603,637,705,748,837,883,931,981,1048,1105,1222,1323,1489,1560,
%U A267767 1684,1744,2028,2185,2254,2346,2401,2500,2601,2763,2869,3084,3136,3249,3364,3547,3667,3865,3969,4096
%N A267767 Numbers whose base-7 representation is a square when read in base 10.
%C A267767 Trivially includes powers of 49, since 49^k = 100..00_7 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 49*a(n) is also in the sequence. One could call "primitive" the terms not of this form. These primitive terms include the subsequence 49^k + 2*7^k + 1 = (7^k+1)^2, k > 0, which yields A033934 when written in base 7.
%H A267767 Chai Wah Wu, <a href="/A267767/b267767.txt">Table of n, a(n) for n = 1..10000</a>
%t A267767 Select[Range[0, 2 10^4], IntegerQ@Sqrt@FromDigits@IntegerDigits[#, 7] &] (* _Vincenzo Librandi_, Dec 28 2016 *)
%o A267767 (PARI) is(n,b=7,c=10)=issquare(subst(Pol(digits(n,b)),x,c))
%o A267767 (Python)
%o A267767 A267767_list = [int(s, 7) for s in (str(i**2) for i in range(10**6)) if max(s) < '7'] # _Chai Wah Wu_, Jan 20 2016
%o A267767 (Magma) [n: n in [0..10^4] | IsSquare(Seqint(Intseq(n, 7)))]; // _Vincenzo Librandi_, Dec 28 2016
%Y A267767 Cf. A267763 - A267769 for bases 3 through 9. The base-2 analog is A000302 = powers of 4.
%Y A267767 For a "prime" analog see also A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924.
%K A267767 nonn,base
%O A267767 1,3
%A A267767 _M. F. Hasler_, Jan 20 2016