

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



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

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: A305842 A094298 A089226 * A310618 A310619 A029641
Adjacent sequences: A102026 A102027 A102028 * A102030 A102031 A102032


KEYWORD

easy,base,nonn


AUTHOR

Jonathan Vos Post, Jun 23 2007


STATUS

approved



