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A279431
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Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 1.
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14
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1^2 = (1), 72^2 = 101000(1)000000, 158^2 = 1100001(1)0000100
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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