A175499 - OEIS

%I #22 Oct 18 2024 17:16:21

%S 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 -13,15,-11,16,-19,17,-9,18,-21,19,-17,20,-18,21,-15,22,-26,23,-16,24,

%U -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 a(n) = A175498(n+1)-A175498(n).

%C No integer occurs in this sequence more than once, by definition. Is this sequence a permutation of the nonzero integers?

%H Chai Wah Wu, <a href="/A175499/b175499.txt">Table of n, a(n) for n = 1..4999</a>

%t a[1] = 0; d[1] = 1; k = 1; z = 10000; zz = 120;

%t A[k_] := Table[a[i], {i, 1, k}]; diff[k_] := Table[d[i], {i, 1, k}];

%t c[k_] := Complement[Range[-z, z], diff[k]];

%t T[k_] := -a[k] + Complement[Range[z], A[k]]

%t Table[{h = Min[Intersection[c[k], T[k]]], a[k + 1] = a[k] + h,

%t    d[k + 1] = h, k = k + 1}, {i, 1, zz}];

%t u = Table[a[k], {k, 1, zz}]  (* A257884 *)

%t Table[d[k], {k, 1, zz}] (* A175499 *)

%t (* _Clark Kimberling_, May 13 2015 *)

%o (Python)

%o A175499_list, l, s, b = [1], 2, 3, set()

%o for n in range(2, 10**2):

%o     i, j = s, s-l

%o     while True:

%o         if not (i in b or j in A175499_list):

%o             A175499_list.append(j)

%o             b.add(i)

%o             l = i

%o             while s in b:

%o                 b.remove(s)

%o                 s += 1

%o             break

%o         i += 1

%o         j += 1 # _Chai Wah Wu_, Dec 15 2014

%o (Haskell)

%o a175499 n = a175499_list !! (n-1)

%o a175499_list = zipWith (-) (tail a175498_list) a175498_list

%o -- _Reinhard Zumkeller_, Apr 25 2015

%Y Cf. A175498, A257884, A131389.

%K sign

%O 1,2

%A _Leroy Quet_, May 31 2010

%E More terms from _Sean A. Irvine_, Jan 27 2011