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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A094298 A338045 A089226 * A310618 A310619 A343501

Adjacent sequences: A102026 A102027 A102028 * A102030 A102031 A102032

Keyword

easy,base,nonn

Author

Jonathan Vos Post, Jun 23 2007

Status

approved