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A033053
Numbers whose base-2 representation Sum_{i=0..m} d(i)*2^i has d(i)=1 when i != m mod 2.
3
1, 3, 6, 7, 13, 15, 26, 27, 30, 31, 53, 55, 61, 63, 106, 107, 110, 111, 122, 123, 126, 127, 213, 215, 221, 223, 245, 247, 253, 255, 426, 427, 430, 431, 442, 443, 446, 447, 490, 491, 494, 495, 506, 507, 510, 511, 853, 855, 861, 863
OFFSET
1,2
COMMENTS
Numbers 2^(2k)-1 - A062880(m) where 2^(2k-2) >= A062880(m) or 2^(2k+1)-1 - A000695(m) where 2^(2k-1) >= A000695(m). - Franklin T. Adams-Watters, Aug 30 2014
LINKS
FORMULA
a(2j+2) = 4 a(j)+3,
a(2j+1) = 4 a(j) + 2 if j <= 3*2^(m-1)-2,
a(2j+1) = 4 a(j) + 1 otherwise, where m = floor(log_2(j+1)).
EXAMPLE
26 = 11010_2 has m=4, and d(i) = 1 for i=1 and 3.
53 = 110101_2 has m=5, and d(i) = 1 for i=0, 2 and 4.
MAPLE
F:= proc(m)
local n0, j, S;
n0:= 2^m + add(2^(m-1-2*j), j=0..floor((m-1)/2));
S:= combinat[powerset]({seq(2^(m-2*j), j=1..floor(m/2))});
map(t -> convert(t, `+`)+n0, S);
end;
`union`(seq(F(m), m=0..24)}; # Robert Israel, Mar 30 2014
CROSSREFS
KEYWORD
nonn,base
EXTENSIONS
Definition corrected, incorrect cross-reference removed, and recurrence formulas by Robert Israel, Mar 30 2014
STATUS
approved