A279431 Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 1.

1, 11, 20, 21, 38, 39, 42, 43, 45, 72, 73, 74, 75, 78, 79, 82, 83, 86, 88, 89, 140, 141, 142, 143, 148, 149, 150, 154, 155, 158, 159, 162, 163, 166, 167, 169, 170, 172, 173, 175, 178, 180, 181, 272, 273, 274, 275, 276, 277, 278, 284, 285, 286, 287, 292, 293

Offset: 1

Author

Lars Blomberg, Jan 07 2017

Keywords

• nonn
• base
• easy

Examples

			1^2 = (1), 72^2 = 101000(1)000000, 158^2 = 1100001(1)0000100
		

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.

Crossrefs

Cf. A279430.

See A279420-A279429 for a base 10 version.

Programs

Mathematica

a[n_]:=Part[IntegerDigits[n, 2], (Length[IntegerDigits[n, 2]] + 1)/2];
Select[Range[0, 293], OddQ[Length[IntegerDigits[#^2, 2]]] && a[#^2]==1 &] (* Indranil Ghosh, Mar 06 2017 *)

PARI

isok(k) = my(d=digits(k^2, 2)); (#d%2 == 1) && (d[#d\2 +1] == 1);
for(k=0, 293, if(isok(k)==1, print1(k,", "))); \\ Indranil Ghosh, Mar 06 2017

Python

i=0
j=1
while i<=293:
    n=str(bin(i**2)[2:])
    l=len(n)
    if l%2 and n[(l-1)//2]=="1":
        print(str(i), end=",")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017