OFFSET
1,1
COMMENTS
Numbers whose binary representation has a prime number of trailing 0's.
a(n)-1 is the sequence of numbers whose binary representation has a prime number of trailing 1's.
Numbers of the form (2^(p+1))*k + 2^p = 2^p * (2*k + 1), where p is prime and k >= 0.
All the terms are divisible by 4.
The asymptotic density of this sequence is Sum_{p prime} 1/2^(p+1) = 0.20734125492555583012... = A051006 / 2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
Select[Range[300], PrimeQ[IntegerExponent[#, 2]] &]
PROG
(PARI) is(n) = isprime(valuation(n, 2));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Feb 23 2024
STATUS
approved