OFFSET
1,10
COMMENTS
a(n) = least number of digits for which the change 0->1 in (binary n) yields a palindrome.
a(n) = Sum_{k=0..A070939(n)/2-1} abs(A030308(n, k) - A030308(n, A070939(n)-k)). - Reinhard Zumkeller, Apr 09 2013
a(n) = Sum_{k=0..A070939(n)/2-1} ((A030308(n, k) + A030308(n, A070939(n)-k)) mod 2). - Reinhard Zumkeller, Sep 18 2013
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
MAPLE
a:= proc(n) local r, ad: r:= proc(s) options operator, arrow: [seq(s[nops(s)-j+1], j = 1 .. nops(s))] end proc: ad := proc(s) local i, j: j := 0: for i to nops(s) do if 0 < abs((s-r(s))[i]) then j := j+1 else end if end do: (1/2)*j end proc: ad(convert(n, base, 2)) end proc: seq(a(n), n = 1 .. 90); # Emeric Deutsch, Aug 20 2016
MATHEMATICA
a[n_] := (bits = IntegerDigits[n, 2]; Total[Abs[bits - Reverse[bits]]]/2); Table[a[n], {n, 1, 90}] (* Jean-François Alcover, Jan 16 2013 *)
PROG
(PARI)
for(n = 1, 90,
v = binary(n); s = 0; j = #v;
for(k=1, #v, s+=abs(v[k]-v[j]); j--);
s/=2;
print1(s, ", ")
)
\\ Washington Bomfim, Jan 13 2011
(Haskell)
a037888 n = div (sum $ map abs $ zipWith (-) bs $ reverse bs) 2
where bs = a030308_row n
-- Reinhard Zumkeller, Apr 09 2013
CROSSREFS
KEYWORD
nonn,base,nice
AUTHOR
STATUS
approved