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A360413 Irregular table T(n, k), n >= 0, k = 1..A002487(n+1), read by rows; the n-th row lists the numbers k such that A065361(k) = n.

%I A360413 #11 Feb 08 2023 14:47:27
%S A360413 0,1,2,3,4,5,6,9,7,10,8,11,12,13,14,15,18,27,16,19,28,17,20,21,29,30,
%T A360413 22,31,23,24,32,33,36,25,34,37,26,35,38,39,40,41,42,45,54,81,43,46,55,
%U A360413 82,44,47,48,56,57,83,84,49,58,85,50,51,59,60,63,86,87,90
%N A360413 Irregular table T(n, k), n >= 0, k = 1..A002487(n+1), read by rows; the n-th row lists the numbers k such that A065361(k) = n.
%C A360413 As a flat sequence, this is a permutation of the nonnegative integers with inverse A360414.
%H A360413 Rémy Sigrist, <a href="/A360413/b360413.txt">Table of n, a(n) for n = 0..9841</a>
%H A360413 Rémy Sigrist, <a href="/A360413/a360413.gp.txt">PARI program</a>
%H A360413 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%H A360413 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A360413 T(n, 1) = A032924(n) for any n > 0.
%F A360413 T(n, A002487(n+1)) = A005836(n+1).
%F A360413 A065361(T(n, k)) = n.
%e A360413 Table T(n, k) begins:
%e A360413   n   n-th row
%e A360413   --  ------------------
%e A360413    0  0
%e A360413    1  1
%e A360413    2  2, 3
%e A360413    3  4
%e A360413    4  5, 6, 9
%e A360413    5  7, 10
%e A360413    6  8, 11, 12
%e A360413    7  13
%e A360413    8  14, 15, 18, 27
%e A360413    9  16, 19, 28
%e A360413   10  17, 20, 21, 29, 30
%e A360413   11  22, 31
%e A360413   12  23, 24, 32, 33, 36
%e A360413 .
%e A360413 Table T(n, k) begins (with terms given in base 3):
%e A360413   n   n-th row in base 3
%e A360413   --  -------------------------
%e A360413    0  0
%e A360413    1  1
%e A360413    2  2, 10
%e A360413    3  11
%e A360413    4  12, 20, 100
%e A360413    5  21, 101
%e A360413    6  22, 102, 110
%e A360413    7  111
%e A360413    8  112, 120, 200, 1000
%e A360413    9  121, 201, 1001
%e A360413   10  122, 202, 210, 1002, 1010
%e A360413   11  211, 1011
%e A360413   12  212, 220, 1012, 1020, 1100
%o A360413 (PARI) See Links section.
%Y A360413 Cf. A002487, A005836, A032924, A065361, A360414 (inverse).
%K A360413 nonn,base,tabf
%O A360413 0,3
%A A360413 _Rémy Sigrist_, Feb 06 2023