A370596 Numbers k such that A007814(k) is a prime number.

4, 8, 12, 20, 24, 28, 32, 36, 40, 44, 52, 56, 60, 68, 72, 76, 84, 88, 92, 96, 100, 104, 108, 116, 120, 124, 128, 132, 136, 140, 148, 152, 156, 160, 164, 168, 172, 180, 184, 188, 196, 200, 204, 212, 216, 220, 224, 228, 232, 236, 244, 248, 252, 260, 264, 268, 276

Offset: 1

Author

Amiram Eldar, Feb 23 2024

Keywords

• nonn
• easy

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

Crossrefs

Cf. A007814, A051006, A359794.

Subsequences: A017113, A051062.

Programs

Mathematica

Select[Range[300], PrimeQ[IntegerExponent[#, 2]] &]

PARI

is(n) = isprime(valuation(n, 2));