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A274524
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Numbers n such that both ror(n) and rol(n) are squares, where ror(x)=A038572(x) is x rotated one binary place to the right, rol(x)=A006257(x) is x rotated one binary place to the left.
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1
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1, 2, 8, 32, 128, 512, 1568, 2048, 2312, 2592, 2888, 8192, 16928, 32768, 131072, 139392, 250632, 524288, 549152, 566048, 672800, 924800, 963272, 1318688, 2097152, 8388608, 8520192, 8769672, 9005768, 12261152, 13582472, 15635232, 33554432, 134217728, 136059008, 136587392
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OFFSET
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1,2
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COMMENTS
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All terms except 1 are even.
Even terms are the numbers of the form n = (a+b)^2/8 such that for some d >= 1,
2^d <= n < 2^(d+1) and 2^(d+1)-1 = a*b. (End)
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LINKS
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MAPLE
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F:= proc(d) local v, R, X;
v:= 2^(d+1)-1;
R:= select(t-> t^2 < v, numtheory:-divisors(v));
op(select(t -> t >= (v+1)/2 and t < v+1, map(t -> (t+ v/t)^2/8, R)));
end proc:
sort(convert({1, seq(F(i), i=1..50)}, list)); # Robert Israel, Jul 13 2016
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MATHEMATICA
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Select[Range[10^6], Times @ Boole@ {IntegerQ@ Sqrt@ FromDigits[RotateRight@ #, 2], IntegerQ@ Sqrt@ FromDigits[RotateLeft@ #, 2]} &@ IntegerDigits[#, 2] == 1 &] (* Michael De Vlieger, Jun 29 2016 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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