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A317407
The "OOPS" numbers -- numbers with ones in all odd-numbered positions of the binary representation of n.
1
1, 2, 3, 5, 7, 10, 11, 14, 15, 21, 23, 29, 31, 42, 43, 46, 47, 58, 59, 62, 63, 85, 87, 93, 95, 117, 119, 125, 127, 170, 171, 174, 175, 186, 187, 190, 191, 234, 235, 238, 239, 250, 251, 254, 255, 341, 343, 349, 351, 373, 375, 381, 383, 469, 471, 477, 479, 501
OFFSET
1,2
COMMENTS
Here we number positions starting with the most significant digit as position 1, and continue to the right down to the least significant digit.
From David A. Corneth, Jul 29 2018: (Start)
1 is in the sequence.
If k is in the sequence then so is 2k+1.
(End)
If A070939(k) is odd and k is in the sequence then so is 2*k. - Robert Israel, Jul 31 2018
LINKS
EXAMPLE
23 is in the sequence because its binary representation is 10111, and it has ones in positions 1,3,5.
MAPLE
S[1]:= [1]:
for n from 2 to 10 do
if n::odd then S[n]:= map(t -> 2*t+1, S[n-1])
else S[n]:= map(t -> (2*t, 2*t+1), S[n-1])
fi
od;
map(op, [seq(S[i], i=1..10)]); # Robert Israel, Jul 31 2018
PROG
(PARI) isok(n) = {my(b=binary(n)); forstep (i=1, #b, 2, if (!b[i], return (0)); ); return (1); } \\ Michel Marcus, Jul 29 2018
CROSSREFS
Sequence in context: A194948 A266679 A285257 * A379929 A191211 A263133
KEYWORD
nonn,base
AUTHOR
Jeffrey Shallit, Jul 28 2018
STATUS
approved