cp's OEIS Frontend

A330385 Add the odd terms and subtract the even ones, the result must always be a square. This is the lexicographically earliest sequence of distinct positive integers with this property.

%I A330385 #11 Dec 12 2019 14:59:01
%S A330385 1,3,4,9,7,12,5,8,15,16,25,11,13,24,39,17,19,21,23,44,36,28,20,33,40,
%T A330385 27,32,45,48,35,85,72,51,64,133,87,60,29,31,105,123,84,41,43,141,96,
%U A330385 47,49,159,57,59,61,63,65,67,69,71,73,75,77,79,81,83,164,156
%N A330385 Add the odd terms and subtract the even ones, the result must always be a square. This is the lexicographically earliest sequence of distinct positive integers with this property.
%C A330385 This sequence is a variant of A329544.
%C A330385 All terms belong to A042965.
%H A330385 Rémy Sigrist, <a href="/A330385/b330385.txt">Table of n, a(n) for n = 1..10000</a>
%H A330385 Rémy Sigrist, <a href="/A330385/a330385.png">Scatterplot of the first 5000000 terms</a>
%e A330385 The first terms, alongside the corresponding running totals, are:
%e A330385   n   a(n)  t(n)
%e A330385   --  ----  --------
%e A330385    1     1   1 = 1^2
%e A330385    2     3   4 = 2^2
%e A330385    3     4   0 = 0^2
%e A330385    4     9   9 = 3^2
%e A330385    5     7  16 = 4^2
%e A330385    6    12   4 = 2^2
%e A330385    7     5   9 = 3^2
%e A330385    8     8   1 = 1^2
%e A330385    9    15  16 = 4^2
%e A330385   10    16   0 = 0^2
%e A330385   11    25  25 = 5^2
%o A330385 (PARI) s=t=0; for (n=1, 65, for (v=1, oo, if (!bittest(s,v) && issquare(u=t-v*(-1)^v), print1 (v", "); s+=2^v; t=u; break)))
%Y A330385 Cf. A000290, A042965, A329544, A330386 (running totals).
%K A330385 nonn,look
%O A330385 1,2
%A A330385 _Rémy Sigrist_, Dec 12 2019