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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}.
37
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
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.
Sequence in context: A331546 A230060 A039025 * A043692 A043775 A043778
KEYWORD
nonn,base,look
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved