cp's OEIS Frontend

A308057 Lexicographically earliest sequence of positive terms such that for any distinct m and n, a(m) + 2*a(m+1) <> a(n) + 2*a(n+1).

%I A308057 #11 May 11 2019 11:40:29
%S A308057 1,1,2,1,3,3,4,1,6,1,7,5,7,7,8,1,12,1,13,8,2,7,12,3,15,10,5,16,3,18,3,
%T A308057 19,12,7,19,14,7,21,15,19,18,6,13,22,6,15,22,8,16,13,24,10,18,15,24,
%U A308057 13,26,13,27,21,25,24,15,30,13,32,13,33,24,18,22,21
%N A308057 Lexicographically earliest sequence of positive terms such that for any distinct m and n, a(m) + 2*a(m+1) <> a(n) + 2*a(n+1).
%C A308057 The sequence becomes linear after some chaotic initial terms.
%H A308057 Rémy Sigrist, <a href="/A308057/b308057.txt">Table of n, a(n) for n = 1..2000</a>
%F A308057 a[n+72] = a[n] + 24 for any n > 847.
%e A308057 The first terms, alongside a(n) + 2*a(n+1), are:
%e A308057   n   a(n)  a(n)+2*a(n+1)
%e A308057   --  ----  -------------
%e A308057    1     1              3
%e A308057    2     1              5
%e A308057    3     2              4
%e A308057    4     1              7
%e A308057    5     3              9
%e A308057    6     3             11
%e A308057    7     4              6
%e A308057    8     1             13
%e A308057    9     6              8
%e A308057   10     1             15
%o A308057 (PARI) s=0; v=1; for(n=1, 72, print1(v", "); for (w=1, oo, if (!bittest(s,x=v+2*w), s+=2^x; v=w; break)))
%Y A308057 See A308058 for the multiplicative variant.
%Y A308057 See A308059 and A308073 for other variants.
%K A308057 nonn
%O A308057 1,3
%A A308057 _Rémy Sigrist_, May 10 2019