cp's OEIS Frontend

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}.

%I A326675 #30 Sep 03 2019 21:14:41
%S A326675 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,
%T A326675 68,69,70,71,72,73,76,77,80,81,82,83,84,85,86,87,88,89,92,93,96,97,
%U A326675 112,113,129,132,133,144,145,148,149,192,193,196,197,208,209,212
%N 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}.
%H A326675 Robert Israel, <a href="/A326675/b326675.txt">Table of n, a(n) for n = 1..10000</a>
%e A326675 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.
%p A326675 extend:= proc(L) local C,c;
%p A326675   C:= select(t -> andmap(s -> igcd(s,t)=1, L), [$1..L[-1]-1]);
%p A326675   L, seq(procname([op(L),c]),c=C)
%p A326675 end proc:
%p A326675 g:= proc(L) local i;
%p A326675   add(2^(i-1),i=L)
%p A326675 end proc:
%p A326675 map(g, [[1],seq(extend([k])[2..-1], k=2..10)]); # _Robert Israel_, Jul 19 2019
%t A326675 Select[Range[100],CoprimeQ@@Join@@Position[Reverse[IntegerDigits[#,2]],1]&]
%o A326675 (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
%Y A326675 Equals the complement of A131577 in A087087.
%Y A326675 Numbers whose prime indices are pairwise coprime are A302696.
%Y A326675 Taking relatively prime instead of pairwise coprime gives A291166.
%Y A326675 Cf. A000120, A051293, A070939, A289509, A291165, A319826, A326669, A326673, A326674.
%K A326675 nonn,base,look
%O A326675 1,2
%A A326675 _Gus Wiseman_, Jul 17 2019