login
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.
3

%I #11 Feb 08 2023 14:47:27

%S 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 22,31,23,24,32,33,36,25,34,37,26,35,38,39,40,41,42,45,54,81,43,46,55,

%U 82,44,47,48,56,57,83,84,49,58,85,50,51,59,60,63,86,87,90

%N 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 As a flat sequence, this is a permutation of the nonnegative integers with inverse A360414.

%H Rémy Sigrist, <a href="/A360413/b360413.txt">Table of n, a(n) for n = 0..9841</a>

%H Rémy Sigrist, <a href="/A360413/a360413.gp.txt">PARI program</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F T(n, 1) = A032924(n) for any n > 0.

%F T(n, A002487(n+1)) = A005836(n+1).

%F A065361(T(n, k)) = n.

%e Table T(n, k) begins:

%e n n-th row

%e -- ------------------

%e 0 0

%e 1 1

%e 2 2, 3

%e 3 4

%e 4 5, 6, 9

%e 5 7, 10

%e 6 8, 11, 12

%e 7 13

%e 8 14, 15, 18, 27

%e 9 16, 19, 28

%e 10 17, 20, 21, 29, 30

%e 11 22, 31

%e 12 23, 24, 32, 33, 36

%e .

%e Table T(n, k) begins (with terms given in base 3):

%e n n-th row in base 3

%e -- -------------------------

%e 0 0

%e 1 1

%e 2 2, 10

%e 3 11

%e 4 12, 20, 100

%e 5 21, 101

%e 6 22, 102, 110

%e 7 111

%e 8 112, 120, 200, 1000

%e 9 121, 201, 1001

%e 10 122, 202, 210, 1002, 1010

%e 11 211, 1011

%e 12 212, 220, 1012, 1020, 1100

%o (PARI) See Links section.

%Y Cf. A002487, A005836, A032924, A065361, A360414 (inverse).

%K nonn,base,tabf

%O 0,3

%A _Rémy Sigrist_, Feb 06 2023