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%I #33 Apr 26 2020 07:40:33
%S 1,2,3,4,6,5,7,8,12,10,14,9,13,11,15,16,24,17,22,18,26,21,28,19,29,20,
%T 27,23,35,30,45,25,34,31,38,32,47,33,44,36,54,37,48,39,57,40,52,41,63,
%U 42,55,43,66,46,65,49,75,51,67,50,70,53,61,56,87,58,82
%N a(1) = 1, and for any n > 0, a(2*n) = a(n) + k(n) and a(2*n+1) = a(n) + 2 * k(n) where k(n) is the least positive integer not leading to a duplicate term.
%C Apparently, every positive integer appears in the sequence.
%H Rémy Sigrist, <a href="/A305410/b305410.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A305410/a305410.png">Scatterplot of (n, a(n)) for n = 1..10000000</a>
%F a(n) = 2*a(2*n) - a(2*n + 1).
%e The first terms, alongside k(n) and associate children, are:
%e n a(n) k(n) a(2*n) a(2*n+1)
%e -- ---- ---- ------ --------
%e 1 1 1 2 3
%e 2 2 2 4 6
%e 3 3 2 5 7
%e 4 4 4 8 12
%e 5 6 4 10 14
%e 6 5 4 9 13
%e 7 7 4 11 15
%e 8 8 8 16 24
%e 9 12 5 17 22
%e 10 10 8 18 26
%o (PARI) lista(nn) = my (a=[1], s=2^a[1]); for (n=1, ceil(nn/2), for (k=1, oo, if (!bittest(s, a[n]+k) && !bittest(s, a[n]+2*k), a=concat(a, [a[n]+k
%o , a[n]+2*k]); s+=2^(a[n]+k) + 2^(a[n]+2*k); break))); a[1..nn]
%Y This sequence is a variant of A322510.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Dec 16 2018
%E Name corrected by _Rémy Sigrist_, Apr 26 2020
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