A317294 Numbers with a noncomposite number of 1's in their binary expansion.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 47, 48, 49, 50, 52, 55, 56, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 79, 80, 81, 82, 84, 87, 88, 91, 93, 94, 96, 97, 98, 100

Offset

1,2

Comments

Union of powers of 2 and pernicious numbers.

All powers of 2 are in the sequence because the binary expansion of a power of 2 contains only one digit "1" and 1 is a noncomposite number (A008578).

If k is in the sequence then so is 2*k. - David A. Corneth, Aug 10 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

8 is in the sequence because the binary expansion of 8 is 1000 and 1000 has one 1, and 1 is a noncomposite number (A008578).
26 is in the sequence because the binary expansion of 26 is 11010 and 11010 has three 1's, and 3 is a noncomposite number.

Maple

filter:= proc(n) local w;
  w:= convert(convert(n, base, 2), `+`);
  w=1 or isprime(w)
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 15 2018

Mathematica

Select[Range[100], !CompositeQ[DigitCount[#, 2, 1]] &] (* Amiram Eldar, Jul 23 2023 *)

Prog

(PARI) is(n) = my(h=hammingweight(n)); ispseudoprime(h) || h==1 \\ Felix Fröhlich, Aug 10 2018

Crossrefs

Union of A000079 and A052294.

The complement is A317295.

All terms of A000051 are in this sequence.

Cf. A000069, A000120, A001969, A008578, A084345.

Sequence in context: A023756 A080944 A321291 * A095736 A004829 A075592

Adjacent sequences: A317291 A317292 A317293 * A317295 A317296 A317297

Keyword

nonn,base,easy

Author

Omar E. Pol, Aug 10 2018

Status

approved