A317295 Numbers with a composite number of 1's in their binary expansion.

15, 23, 27, 29, 30, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60, 63, 71, 75, 77, 78, 83, 85, 86, 89, 90, 92, 95, 99, 101, 102, 105, 106, 108, 111, 113, 114, 116, 119, 120, 123, 125, 126, 135, 139, 141, 142, 147, 149, 150, 153, 154, 156, 159, 163, 165, 166, 169, 170, 172, 175, 177, 178, 180, 183, 184, 187, 189, 190

Offset: 1

Author

Omar E. Pol, Aug 10 2018

Keywords

• nonn
• base
• easy

Comments

By definition no power of 2 is in the sequence.

Examples

			23 is in the sequence because the binary expansion of 23 is 10111 and 10111 has four 1's, and 4 is a composite number (A002808).
		

Links

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

Crossrefs

Complement of A317294.

Cf. A000069, A000120, A001969, A002808, A014312, A052294, A084345.

Programs

Mathematica

Select[Range[200], CompositeQ[DigitCount[#, 2, 1]] &] (* Amiram Eldar, Jul 23 2023 *)

PARI

isok(n) = my(w = hammingweight(n)); (w != 1) && !isprime(w); \\ Michel Marcus, Aug 15 2018

Python

from sympy import isprime; isok = lambda n: n & (n-1) and not isprime(bin(n).count('1')) # David Radcliffe, Aug 15 2018