A334344 Binary Moran numbers: numbers k such that k divided by its binary weight (A000120) is a prime number.

2, 6, 10, 21, 34, 55, 69, 92, 115, 116, 155, 172, 185, 205, 212, 222, 246, 284, 295, 318, 321, 332, 355, 356, 366, 395, 404, 438, 452, 474, 498, 514, 535, 556, 565, 596, 606, 623, 652, 749, 788, 822, 835, 865, 889, 905, 973, 978, 1041, 1052, 1076, 1086, 1108, 1124

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

2 is a term since its binary weight is 1 and 2/1 = 2, which is a prime number.
6 (110 in binary) has a binary weight of 2 and 6/2 = 3, which is prime, so 6 is also in the sequence. Likewise 10 (1010 in binary) also has a binary weight of 2, and 10/2 = 5, which is prime, so 10 is also in the sequence.
14 (1110 in binary) has binary weight of 3. But 14/3 is not prime, so 14 is not in the sequence.

Maple

q:= n-> (p-> is(p, integer) and isprime(p))(n/add(i, i=Bits[Split](n))):
select(q, [$1..1200])[];  # Alois P. Heinz, Apr 23 2020

Mathematica

Select[Range[1000], PrimeQ[# / DigitCount[#, 2, 1]] &]

Prog

(Scala) def isPrime(num: Int): Boolean = Math.abs(num) match {
  case 0 => false; case 1 => false; case n => (2 to Math.floor(Math.sqrt(n)).toInt) forall (p => n % p != 0)
}
(1 to 1000).filter{ n => val binWt = Integer.bitCount(n); (n % binWt) == 0 && isPrime(n / binWt) } // Alonso del Arte, Apr 23 2020
(PARI) isok(m) = iferr(isprime(m/hammingweight(m)), E, 0); \\ Michel Marcus, Apr 24 2020

Crossrefs

Subsequence of A049445.

Cf. A000120, A001101.

Sequence in context: A083176 A103628 A207382 * A272952 A034450 A297185

Adjacent sequences: A334341 A334342 A334343 * A334345 A334346 A334347

Keyword

nonn,base

Author

Amiram Eldar, Apr 23 2020

Status

approved