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A279430 Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 0.

%I A279430 #22 Dec 23 2024 14:53:45
%S A279430 0,2,4,5,8,9,10,16,17,18,19,22,32,33,34,35,36,37,40,41,44,64,65,66,67,
%T A279430 68,69,70,71,76,77,80,81,84,85,87,90,128,129,130,131,132,133,134,135,
%U A279430 136,137,138,139,144,145,146,147,151,152,153,156,157,160,161,164
%N A279430 Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 0.
%H A279430 Lars Blomberg, <a href="/A279430/b279430.txt">Table of n, a(n) for n = 1..10000</a>
%H A279430 Andrew Weimholt, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2016-December/017140.html">Middle digit in square numbers</a>, Seqfan Mailing list, Dec 12 2016.
%t A279430 a[n_]:=Part[IntegerDigits[n,2],(Length[IntegerDigits[n,2]]+1)/2];
%t A279430 Select[Range[0,164],OddQ[Length[IntegerDigits[#^2,2]]] && a[#^2]==0 &] (* _Indranil Ghosh_, Mar 06 2017 *)
%t A279430 k2oQ[n_]:=Module[{idn=IntegerDigits[n^2,2],len},len=Length[idn];OddQ[ len] && idn[[(len+1)/2]]==0]; Select[Range[0,200],k2oQ] (* _Harvey P. Dale_, Jan 29 2020 *)
%o A279430 (PARI) isok(k) = my(d=digits(k^2, 2)); (#d%2 == 1) && (d[#d\2 +1] == 0);
%o A279430 for(k=0, 164, if(k==0 || isok(k)==1, print1(k,", "))); \\ _Indranil Ghosh_, Mar 06 2017
%o A279430 (Python)
%o A279430 i=0
%o A279430 j=1
%o A279430 while i<=164:
%o A279430     n=str(bin(i**2)[2:])
%o A279430     l=len(n)
%o A279430     if l%2 and n[(l-1)//2]=="0":
%o A279430         print(str(i), end=",")
%o A279430         j+=1
%o A279430     i+=1 # _Indranil Ghosh_, Mar 06 2017
%Y A279430 Cf. A279431.
%Y A279430 See A279420-A279429 for a base-10 version.
%K A279430 nonn,base,easy
%O A279430 1,2
%A A279430 _Lars Blomberg_, Jan 07 2017