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A033053 Numbers n such that base 2 representation Sum{d(i)*2^i: i=0,1,...,m} 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 (list; graph; refs; listen; history; text; internal format)
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

Robert Israel, Table of n, a(n) for n = 1..12286

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

Cf. A126684, A000695, A062880.

Sequence in context: A176301 A191290 A137595 * A248388 A107850 A216514

Adjacent sequences:  A033050 A033051 A033052 * A033054 A033055 A033056

KEYWORD

nonn,base

AUTHOR

Clark Kimberling

EXTENSIONS

Definition corrected, incorrect cross-reference removed, and recurrence formulas by Robert Israel, Mar 30 2014

STATUS

approved

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Last modified February 19 03:37 EST 2018. Contains 299330 sequences. (Running on oeis4.)