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A182209 a(n) is the least m >= n, such that the Hamming distance D(n,m) = 3. 2
7, 6, 5, 4, 9, 8, 8, 9, 15, 14, 13, 12, 16, 17, 18, 19, 23, 22, 21, 20, 25, 24, 24, 25, 31, 30, 29, 28, 36, 37, 38, 39, 39, 38, 37, 36, 41, 40, 40, 41, 47, 46, 45, 44, 48, 49, 50, 51, 55, 54, 53, 52, 57, 56, 56, 57, 63, 62, 61, 60, 76, 77, 78, 79, 71, 70, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = n<+>3 (see comment in A206853).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

If n==i mod 8, then a(n) = n-2*i+7, i=0,1,2,3;  if n==4 mod 16, then a(n) = n+5; if n==12 mod 16, then  a(n) = n+2^(A007814(n+4)-2); if n==5 mod 16, then a(n) = n+3; if n==13 mod 16, then  a(n) = n+2^(A007814(n+3)-2); if n==6 mod 8, then a(n) = n+2^(A007814(n+2)-2); if n==7 mod 8, then a(n) = n+2^(A007814(n+1)-2).

Using this formula, we can prove conjecture formulated in comment in A209554 in case k=3. Moreover, one can proved that N could be represented in form n<+>2 or n<+>3 iff N is not a number of the forms 32*t, 32*t+1. - Vladimir Shevelev, Apr 25 2012

MAPLE

HD:= proc(i, j) local d, n, m; d, n, m:= 0, i, j;

       while n>0 or m>0 do

           d:= d +abs(irem(n, 2, 'n') -irem(m, 2, 'm'))

       od; d

     end:

a:= proc(n) local c;

      for c from n do if HD(n, c)=3 then return c fi od

    end:

seq (a(n), n=0..100); # Alois P. Heinz, Apr 18 2012

CROSSREFS

Cf. A205509, A205510, A205511, A205302, A205649, A205533, A122565, A206852, A206853, A206960, A207063, A209544, A209554, A007814, A086799, A182187.

Sequence in context: A055118 A132671 A074921 * A120634 A178753 A104178

Adjacent sequences:  A182206 A182207 A182208 * A182210 A182211 A182212

KEYWORD

nonn,base

AUTHOR

Vladimir Shevelev, Apr 18 2012

STATUS

approved

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Last modified April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)