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A308732
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Primes p such that the smallest possible number of 1's in binary representation of a multiple of p equals 3.
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1
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7, 23, 47, 71, 73, 79, 103, 151, 167, 191, 199, 239, 263, 271, 311, 337, 359, 367, 383, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 919, 937, 967, 983, 991, 1031, 1039, 1063, 1087, 1151, 1223, 1231, 1279, 1289, 1303
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OFFSET
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1,1
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COMMENTS
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The first few corresponding multipliers that give three 1's are (for the numbers listed above) are 1, 3, 11, 119, 1, 13, 5, 7, 791, 87839, 247, 17970575, 3987, 8048111, 7, 49, 23, 2995944847, 5607007, 7, 2319663.
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LINKS
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MAPLE
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filter:= proc(n) local S, r, j;
if not isprime(n) then return false fi;
r:= numtheory:-order(2, n);
if r::even then return false fi;
S:= {seq(2 &^ j mod n, j=1..r)};
S intersect map(t -> -t-1 mod n, S) <> {}
end proc:
select(filter, [seq(i, i=3..2000, 2)]); # Robert Israel, Jun 23 2019
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CROSSREFS
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Cf. A014662, which enumerates the same sequence for two 1's instead of three.
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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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