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A380123 Irregular table T(n, k), n >= 0, k = 1..A380122(n), read by rows; the n-th row lists the integers m (possibly negative) such that the nonzero digits in the nonadjacent form for m appear in the nonadjacent form for n.

%I A380123 #10 Jan 14 2025 09:06:43
%S A380123 0,0,1,0,2,-1,0,3,4,0,4,0,1,4,5,-2,0,6,8,-1,0,7,8,0,8,0,1,8,9,0,2,8,
%T A380123 10,-5,-4,-1,0,11,12,15,16,-4,0,12,16,-4,-3,0,1,12,13,16,17,-2,0,14,
%U A380123 16,-1,0,15,16,0,16,0,1,16,17,0,2,16,18,-1,0,3,4,15,16,19,20
%N A380123 Irregular table T(n, k), n >= 0, k = 1..A380122(n), read by rows; the n-th row lists the integers m (possibly negative) such that the nonzero digits in the nonadjacent form for m appear in the nonadjacent form for n.
%H A380123 Rémy Sigrist, <a href="/A380123/b380123.txt">Table of n, a(n) for n = 0..6724</a> (rows for n = 0..2^9 flattened)
%H A380123 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, pages 61-62.
%H A380123 Wikipedia, <a href="https://en.wikipedia.org/wiki/Non-adjacent_form">Non-adjacent form</a>
%F A380123 T(n, 1) = A184616(n).
%F A380123 T(n, A380122(n)) = n.
%e A380123 Irregular table T(n, k) begins:
%e A380123   n   n-th row
%e A380123   --  -----------------------------
%e A380123    0  0
%e A380123    1  0, 1
%e A380123    2  0, 2
%e A380123    3  -1, 0, 3, 4
%e A380123    4  0, 4
%e A380123    5  0, 1, 4, 5
%e A380123    6  -2, 0, 6, 8
%e A380123    7  -1, 0, 7, 8
%e A380123    8  0, 8
%e A380123    9  0, 1, 8, 9
%e A380123   10  0, 2, 8, 10
%e A380123   11  -5, -4, -1, 0, 11, 12, 15, 16
%e A380123   12  -4, 0, 12, 16
%e A380123   13  -4, -3, 0, 1, 12, 13, 16, 17
%e A380123   14  -2, 0, 14, 16
%e A380123   15  -1, 0, 15, 16
%e A380123   16  0, 16
%e A380123 .
%e A380123 Irregular table T(n, k) begins in nonadjacent form:
%e A380123   n      n-th row
%e A380123   -----  ------------------------------------------
%e A380123       0  0
%e A380123       1  0, 1
%e A380123      10  0, 10
%e A380123     10T  T, 0, 10T, 100
%e A380123     100  0, 100
%e A380123     101  0, 1, 100, 101
%e A380123    10T0  T0, 0, 10T0, 1000
%e A380123    100T  T, 0, 100T, 1000
%e A380123    1000  0, 1000
%e A380123    1001  0, 1, 1000, 1001
%e A380123    1010  0, 10, 1000, 1010
%e A380123   10T0T  T0T, T00, T, 0, 10T0T, 10T00, 1000T, 10000
%e A380123   10T00  T00, 0, 10T00, 10000
%o A380123 (PARI) row(n) = { my (r = [0], d, b = 1); while (n, if (n % 2, n -= d = 2 - (n%4); r = concat(r, [v + d*b | v <- r]);); n /= 2; b *= 2;); vecsort(r); }
%Y A380123 See A295989 for a similar sequence.
%Y A380123 Cf. A184616, A380122.
%K A380123 sign,base,tabf
%O A380123 0,5
%A A380123 _Rémy Sigrist_, Jan 12 2025