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

1,1

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

Cf. A007814, A051006, A359794.

Subsequences: A017113, A051062.

Sequence in context: A311651 A311652 A311653 * A171949 A217319 A133466

Adjacent sequences: A370593 A370594 A370595 * A370597 A370598 A370599

Keyword

nonn,easy

Author

Amiram Eldar, Feb 23 2024

Status

approved