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A377388 Infinite sequence of integers a(1), a(2), ... such that for any n > 0, a(n) is as small as possible (in absolute value) and the means of consecutive terms are all distinct; in case of a tie, preference is given to the positive value.

%I A377388 #10 Oct 28 2024 16:24:26
%S A377388 0,1,-2,-3,-5,-8,-6,-11,-13,-21,-16,9,-42,-24,-25,-27,-34,-35,-46,10,
%T A377388 2,90,42,31,26,11,30,18,58,41,20,86,43,60,45,103,48,54,105,83,-48,
%U A377388 -151,-155,-59,-87,-79,-146,106,-157,-109,-218,-208,-88,-45,-99,-131,27
%N A377388 Infinite sequence of integers a(1), a(2), ... such that for any n > 0, a(n) is as small as possible (in absolute value) and the means of consecutive terms are all distinct; in case of a tie, preference is given to the positive value.
%C A377388 This sequence is a variant of A377351 allowing negative values.
%C A377388 All terms are distinct.
%H A377388 Rémy Sigrist, <a href="/A377388/b377388.txt">Table of n, a(n) for n = 1..10000</a>
%H A377388 Rémy Sigrist, <a href="/A377388/a377388.txt">C++ program</a>
%e A377388 The first terms, alongside the means of consecutive terms ending with a(n), are:
%e A377388   n  a(n)  Corresponding means
%e A377388   -  ----  -----------------------------------------
%e A377388   1     0  0
%e A377388   2     1  1/2, 1
%e A377388   3    -2  -1/3, -1/2, -2
%e A377388   4    -3  -1, -4/3, -5/2, -3
%e A377388   5    -5  -9/5, -9/4, -10/3, -4, -5
%e A377388   6    -8  -17/6, -17/5, -9/2, -16/3, -13/2, -8
%e A377388   7    -6  -23/7, -23/6, -24/5, -11/2, -19/3, -7, -6
%o A377388 (C++) // See Links section.
%o A377388 (Python)
%o A377388 from fractions import Fraction
%o A377388 from itertools import count, islice
%o A377388 def A377388gen(): # generator of terms
%o A377388     alst, means_seen = [0], {0}
%o A377388     while True:
%o A377388         yield alst[-1]
%o A377388         for i in count(1):
%o A377388             failed = True
%o A377388             for k in [i, -i]:
%o A377388                 if k in means_seen: continue
%o A377388                 mk, failed, sk = {k}, False, k
%o A377388                 for j in range(1, len(alst)+1):
%o A377388                     sk += alst[-j]
%o A377388                     m = Fraction(sk, j+1)
%o A377388                     if m in means_seen or m in mk: failed = True; break
%o A377388                     mk.add(m)
%o A377388                 if not failed:
%o A377388                     means_seen |= mk
%o A377388                     alst.append(k)
%o A377388                     break
%o A377388             if not failed: break
%o A377388 print(list(islice(A377388gen(), 60))) # _Michael S. Branicky_, Oct 27 2024, Oct 28 2024
%Y A377388 Cf. A377351, A377389.
%K A377388 sign
%O A377388 1,3
%A A377388 _Rémy Sigrist_, Oct 27 2024