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A175499 a(n) = A175498(n+1)-A175498(n).

%I A175499 #22 Oct 18 2024 17:16:21
%S A175499 1,2,-1,3,4,-5,6,-4,5,-3,7,-8,9,-2,8,-10,11,-6,10,-14,12,-7,13,-12,14,
%T A175499 -13,15,-11,16,-19,17,-9,18,-21,19,-17,20,-18,21,-15,22,-26,23,-16,24,
%U A175499 -29,25,-22,27,-23,26,-25,28,-27,29,-28,30,-24,31,-35,32,33,-62,34,-31,35,-34,36,-33,37,-39,38,-32,39,-42,40,-36
%N A175499 a(n) = A175498(n+1)-A175498(n).
%C A175499 No integer occurs in this sequence more than once, by definition. Is this sequence a permutation of the nonzero integers?
%H A175499 Chai Wah Wu, <a href="/A175499/b175499.txt">Table of n, a(n) for n = 1..4999</a>
%t A175499 a[1] = 0; d[1] = 1; k = 1; z = 10000; zz = 120;
%t A175499 A[k_] := Table[a[i], {i, 1, k}]; diff[k_] := Table[d[i], {i, 1, k}];
%t A175499 c[k_] := Complement[Range[-z, z], diff[k]];
%t A175499 T[k_] := -a[k] + Complement[Range[z], A[k]]
%t A175499 Table[{h = Min[Intersection[c[k], T[k]]], a[k + 1] = a[k] + h,
%t A175499    d[k + 1] = h, k = k + 1}, {i, 1, zz}];
%t A175499 u = Table[a[k], {k, 1, zz}]  (* A257884 *)
%t A175499 Table[d[k], {k, 1, zz}] (* A175499 *)
%t A175499 (* _Clark Kimberling_, May 13 2015 *)
%o A175499 (Python)
%o A175499 A175499_list, l, s, b = [1], 2, 3, set()
%o A175499 for n in range(2, 10**2):
%o A175499     i, j = s, s-l
%o A175499     while True:
%o A175499         if not (i in b or j in A175499_list):
%o A175499             A175499_list.append(j)
%o A175499             b.add(i)
%o A175499             l = i
%o A175499             while s in b:
%o A175499                 b.remove(s)
%o A175499                 s += 1
%o A175499             break
%o A175499         i += 1
%o A175499         j += 1 # _Chai Wah Wu_, Dec 15 2014
%o A175499 (Haskell)
%o A175499 a175499 n = a175499_list !! (n-1)
%o A175499 a175499_list = zipWith (-) (tail a175498_list) a175498_list
%o A175499 -- _Reinhard Zumkeller_, Apr 25 2015
%Y A175499 Cf. A175498, A257884, A131389.
%K A175499 sign
%O A175499 1,2
%A A175499 _Leroy Quet_, May 31 2010
%E A175499 More terms from _Sean A. Irvine_, Jan 27 2011