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

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

Offset: 1

Author

Leroy Quet, May 31 2010

Keywords

• sign

Comments

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..4999

Crossrefs

Cf. A175498, A257884, A131389.

Programs

Haskell

a175499 n = a175499_list !! (n-1)
a175499_list = zipWith (-) (tail a175498_list) a175498_list
-- Reinhard Zumkeller, Apr 25 2015

Mathematica

a[1] = 0; d[1] = 1; k = 1; z = 10000; zz = 120;
A[k_] := Table[a[i], {i, 1, k}]; diff[k_] := Table[d[i], {i, 1, k}];
c[k_] := Complement[Range[-z, z], diff[k]];
T[k_] := -a[k] + Complement[Range[z], A[k]]
Table[{h = Min[Intersection[c[k], T[k]]], a[k + 1] = a[k] + h,
   d[k + 1] = h, k = k + 1}, {i, 1, zz}];
u = Table[a[k], {k, 1, zz}]  (* A257884 *)
Table[d[k], {k, 1, zz}] (* A175499 *)
(* Clark Kimberling, May 13 2015 *)

Python

A175499_list, l, s, b = [1], 2, 3, set()
for n in range(2, 10**2):
    i, j = s, s-l
    while True:
        if not (i in b or j in A175499_list):
            A175499_list.append(j)
            b.add(i)
            l = i
            while s in b:
                b.remove(s)
                s += 1
            break
        i += 1
        j += 1 # Chai Wah Wu, Dec 15 2014

Extensions

More terms from Sean A. Irvine, Jan 27 2011