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A206853 a(1)=1, for n>1, a(n) is the least number > a(n-1) such that the Hamming distance D(a(n-1), a(n)) = 2. 21
1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 31, 47, 55, 59, 61, 62, 94, 110, 118, 122, 124, 127, 191, 223, 239, 247, 251, 253, 254, 382, 446, 478, 494, 502, 506, 508, 511, 767, 895, 959, 991, 1007, 1015, 1019, 1021, 1022, 1534, 1790, 1918, 1982, 2014, 2030, 2038, 2042 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For integers a, b, denote by a<+>b the least c>=a, such that D(a,c)=b (note that, generally speaking, a<+>b differs from b<+>a). Then a(n+1)=a(n)<+>2. Thus this sequence is a Hamming analog of odd numbers 1,3,5,...
A Hamming analog of nonnegative integers is A000225 and a Hamming analog of the triangular numbers is A000975.
All terms are odious (A000069).
LINKS
MAPLE
read("transforms");
Hamming := proc(a, b)
XORnos(a, b) ;
wt(%) ;
end proc:
Dplus := proc(a, b)
for c from a to 1000000 do
if Hamming(a, c)=b then
return c;
end if;
end do:
return -1 ;
end proc:
A206853 := proc(n)
option remember;
if n = 1 then
1;
else
Dplus(procname(n-1), 2) ;
end if;
end proc: # R. J. Mathar, Apr 05 2012
MATHEMATICA
myHammingDistance[n_, m_] := Module[{g = Max[m, n], h = Min[m, n]}, b1 = IntegerDigits[g, 2]; b2 = IntegerDigits[h, 2, Length[b1]]; HammingDistance[b1, b2]]; t = {1}; Do[If[myHammingDistance[t[[-1]], n] == 2, AppendTo[t, n]], {n, 2, 2042}]; t (* T. D. Noe, Mar 07 2012 *)
t={x=1}; Do[i=x+1; While[Count[IntegerDigits[BitXor[x, i], 2], 1]!=2, i++]; AppendTo[t, x=i], {n, 53}]; t (* Jayanta Basu, May 26 2013 *)
PROG
(PARI) next_A206853(n)={my(b=binary(n)); until(norml2(binary(n)-b)==2, n++>=2^#b & b=concat(0, b)); n}
print1(n=1); for(i=1, 99, print1(", "n=next_A206853(n))) \\ M. F. Hasler, Apr 07 2012
CROSSREFS
Cf. A182187 (n<+>2), A207063 (starting from 0).
Sequence in context: A249594 A127575 A240106 * A229618 A087285 A107791
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Feb 13 2012
STATUS
approved

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Last modified June 23 15:10 EDT 2024. Contains 373651 sequences. (Running on oeis4.)