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.

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

Offset: 1

Author

Jonathan Vos Post, Jun 23 2007

Keywords

• easy
• base
• nonn

Comments

Semiprime analog of A061712. Extended by Stefan Steinerberger. Includes the subset Mersenne semiprimes A092561.

Examples

			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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..250

Crossrefs

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

Programs

Mathematica

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