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

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, 68, 69, 70, 71, 76, 77, 80, 81, 84, 85, 87, 90, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 145, 146, 147, 151, 152, 153, 156, 157, 160, 161, 164

Offset

1,2

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000

Andrew Weimholt, Middle digit in square numbers, Seqfan Mailing list, Dec 12 2016.

Mathematica

a[n_]:=Part[IntegerDigits[n, 2], (Length[IntegerDigits[n, 2]]+1)/2];
Select[Range[0, 164], OddQ[Length[IntegerDigits[#^2, 2]]] && a[#^2]==0 &] (* Indranil Ghosh, Mar 06 2017 *)
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 *)

Prog

(PARI) isok(k) = my(d=digits(k^2, 2)); (#d%2 == 1) && (d[#d\2 +1] == 0);
for(k=0, 164, if(k==0 || isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017
(Python)
i=0
j=1
while i<=164:
    n=str(bin(i**2)[2:])
    l=len(n)
    if l%2 and n[(l-1)//2]=="0":
        print(str(i), end=", ")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

Crossrefs

Cf. A279431.

See A279420-A279429 for a base-10 version.

Sequence in context: A166021 A339906 A359267 * A003714 A340956 A010402

Adjacent sequences: A279427 A279428 A279429 * A279431 A279432 A279433

Keyword

nonn,base,easy

Author

Lars Blomberg, Jan 07 2017

Status

approved