A326675 The positions of 1's in the reversed binary expansion of n are pairwise coprime, where a singleton is not coprime unless it is {1}.

1, 3, 5, 6, 7, 9, 12, 13, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 33, 48, 49, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 96, 97, 112, 113, 129, 132, 133, 144, 145, 148, 149, 192, 193, 196, 197, 208, 209, 212

Offset: 1

Author

Gus Wiseman, Jul 17 2019

Keywords

• nonn
• base
• look

Examples

			41 has reversed binary expansion (1,0,0,1,0,1) with positions of 1's being {1,4,6}, which are not pairwise coprime, so 41 is not in the sequence.
		

Links

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

Crossrefs

Equals the complement of A131577 in A087087.

Numbers whose prime indices are pairwise coprime are A302696.

Taking relatively prime instead of pairwise coprime gives A291166.

Cf. A000120, A051293, A070939, A289509, A291165, A319826, A326669, A326673, A326674.

Programs

Maple

extend:= proc(L) local C,c;
  C:= select(t -> andmap(s -> igcd(s,t)=1, L), [$1..L[-1]-1]);
  L, seq(procname([op(L),c]),c=C)
end proc:
g:= proc(L) local i;
  add(2^(i-1),i=L)
end proc:
map(g, [[1],seq(extend([k])[2..-1], k=2..10)]); # Robert Israel, Jul 19 2019

Mathematica

Select[Range[100],CoprimeQ@@Join@@Position[Reverse[IntegerDigits[#,2]],1]&]

PARI

is(n) = my (p=1); while (n, my (o=1+valuation(n,2)); if (gcd(p,o)>1, return (0), n-=2^(o-1); p*=o)); return (1) \\ Rémy Sigrist, Jul 19 2019