A317295 -id:A317295 - cp's OEIS frontend

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

Omar E. Pol, Aug 10 2018

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

			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.

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

Union of A000079 and A052294.
The complement is A317295.
All terms of A000051 are in this sequence.
Cf. A000069, A000120, A001969, A008578, A084345.

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

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

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

cp's OEIS Frontend

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

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