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A380174 a(n) is the least integer (in absolute value) not among the n initial terms of A377091; in case of a tie, preference is given to the positive value.

%I A380174 #24 Jan 17 2025 09:10:53
%S A380174 0,1,-1,-1,-1,3,-3,-3,-3,-3,-5,-5,-5,-5,-5,-5,-5,9,9,9,9,9,9,10,11,12,
%T A380174 -13,14,14,14,14,14,14,14,15,16,17,19,19,19,19,19,19,19,19,19,19,22,
%U A380174 22,24,24,24,24,-25,-26,-27,-28,29,29,29,29,29,29,29,29,33
%N A380174 a(n) is the least integer (in absolute value) not among the n initial terms of A377091; in case of a tie, preference is given to the positive value.
%C A380174 If abs(A377091(n-1) - a(n)) is a square number for some n > 0, then A377091(n) = a(n).
%H A380174 Rémy Sigrist, <a href="/A380174/b380174.txt">Table of n, a(n) for n = 0..10000</a>
%H A380174 Rémy Sigrist, <a href="/A380174/a380174.gp.txt">PARI program</a>
%F A380174 abs(a(n)) = min(A379067(n-1), A379068(n-1)) for any n > 0.
%e A380174 The initial terms are:
%e A380174   n   a(n)  n initial terms of A377091
%e A380174   --  ----  ----------------------------------
%e A380174    0     0  {}
%e A380174    1     1  {0}
%e A380174    2    -1  {0, 1}
%e A380174    3    -1  {0, 1, 2}
%e A380174    4    -1  {-2, 0, 1, 2}
%e A380174    5     3  {-2, -1, 0, 1, 2}
%e A380174    6    -3  {-2, -1, 0, 1, 2, 3}
%e A380174    7    -3  {-2, -1, 0, 1, 2, 3, 4}
%e A380174    8    -3  {-2, -1, 0, 1, 2, 3, 4, 5}
%e A380174    9    -3  {-4, -2, -1, 0, 1, 2, 3, 4, 5}
%e A380174   10    -5  {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
%o A380174 (PARI) \\ See Links section.
%Y A380174 See A379067 and A379068 for similar sequences.
%Y A380174 Cf. A377091.
%K A380174 sign
%O A380174 0,6
%A A380174 _Rémy Sigrist_, Jan 15 2025