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

1,2

Links

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

Example

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.

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]&]

Prog

(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

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.

Sequence in context: A331546 A230060 A039025 * A043692 A043775 A043778

Adjacent sequences: A326672 A326673 A326674 * A326676 A326677 A326678

Keyword

nonn,base,look

Author

Gus Wiseman, Jul 17 2019

Status

approved