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 A102029 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. 1

%I

%S 4,6,14,15,55,95,247,447,511,1535,2047,7167,12287,32255,49151,98303,

%T 196607,393215,983039,1572863,3145727,6291455,8388607,33423359,

%U 50331647,117440511,201326591,528482303,805306367,1879048191,3221225471

%N 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.

%C Semiprime analog of A061712. Extended by _Stefan Steinerberger_. Includes the subset Mersenne semiprimes A092561.

%H Donovan Johnson, <a href="/A102029/b102029.txt">Table of n, a(n) for n = 1..250</a>

%e 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.

%e a(2) = 6 since A001358(2) = 6 = 110 (base 2) has exactly 2 ones.

%e 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.

%t Join[{4},Table[SelectFirst[Sort[FromDigits[#,2]&/@Permutations[ Join[ PadRight[{}, n,1],{0}]]],PrimeOmega[#]==2&],{n,2,40}]] (* _Harvey P. Dale_, Feb 06 2015 *)

%Y Cf. A000043, A000120, A000337, A000668, A001358, A007088, A061712, A085724, A089226, A089998, A089999, A091991, A092558, A092559, A092561, A092562, A081093, A102782, A110472, A110699, A110700.

%K easy,base,nonn

%O 1,1

%A _Jonathan Vos Post_, Jun 23 2007

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Last modified February 22 12:24 EST 2020. Contains 332135 sequences. (Running on oeis4.)