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A279431
Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 1.
14
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
1,2
LINKS
Andrew Weimholt, Middle digit in square numbers, Seqfan Mailing list, Dec 12 2016.
EXAMPLE
1^2 = (1), 72^2 = 101000(1)000000, 158^2 = 1100001(1)0000100
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 *)
PROG
(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
CROSSREFS
Cf. A279430.
See A279420-A279429 for a base 10 version.
Sequence in context: A105958 A124250 A124251 * A230541 A053715 A343770
KEYWORD
nonn,base,easy
AUTHOR
Lars Blomberg, Jan 07 2017
STATUS
approved