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A102029
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Smallest semiprime with Hamming weight n (i.e., smallest semiprime with exactly n ones when written in binary), or -1 if no such number exists.
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2
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4, 6, 14, 15, 55, 95, 247, 447, 511, 1535, 2047, 7167, 12287, 32255, 49151, 98303, 196607, 393215, 983039, 1572863, 3145727, 6291455, 8388607, 33423359, 50331647, 117440511, 201326591, 528482303, 805306367, 1879048191, 3221225471
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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a(1) = 4 because the first semiprime A001358(1) is 4 (base 10) which is written 100 in binary, the latter representation having exactly 1 one.
a(2) = 6 since A001358(2) = 6 = 110 (base 2) has exactly 2 ones.
a(4) = 15 since A001358(6) = 15 = 1111 (base 2) has exactly 4 ones and, as it also has no zeros, is the smallest of the Mersenne semiprimes.
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MATHEMATICA
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Join[{4}, Table[SelectFirst[Sort[FromDigits[#, 2]&/@Permutations[ Join[ PadRight[{}, n, 1], {0}]]], PrimeOmega[#]==2&], {n, 2, 40}]] (* Harvey P. Dale, Feb 06 2015 *)
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CROSSREFS
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Cf. A000043, A000120, A000337, A000668, A001358, A007088, A061712, A085724, A089226, A089998, A089999, A091991, A092558, A092559, A092561, A092562, A081093, A102782, A110472, A110699, A110700.
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KEYWORD
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easy,base,nonn
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AUTHOR
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STATUS
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approved
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