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%I #15 Apr 01 2024 12:09:49
%S 0,1,2,3,4,5,9,6,7,8,10,11,12,13,14,27,15,16,26,28,17,19,20,21,24,25,
%T 29,30,18,22,23,31,32,36,33,34,35,37,38,39,40,41,81,42,43,80,82,44,46,
%U 47,48,78,79,83,84,45,49,77,85,50,58,59,63,72,76,86,90
%N Irregular triangle T(n, k), n >= 0, read by rows; the n-th row lists the numbers m such that A371263(m) = n.
%C Row 0 has 1 term; for n > 0, row n has A225081(n-1) terms.
%C As a flat sequence, this is a permutation of the nonnegative integers, with inverse A371266.
%H Rémy Sigrist, <a href="/A371265/b371265.txt">Table of n, a(n) for n = 0..9841</a>
%H Rémy Sigrist, <a href="/A371265/a371265.gp.txt">PARI program</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e Triangle 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, 9
%e 5 6, 7, 8, 10
%e 6 11, 12
%e 7 13
%e 8 14, 27
%e 9 15, 16, 26, 28
%e 10 17, 19, 20, 21, 24, 25, 29, 30
%e 11 18, 22, 23, 31
%e 12 32, 36
%e 13 33, 34, 35, 37
%e 14 38, 39
%e 15 40
%e .
%e Triangle T(n, k) begins, in balanced ternary, with row indexes in binary:
%e bin(n) n-th row in balanced ternary
%e ------ ----------------------------------------------
%e 0 0
%e 1 1
%e 10 1T, 10
%e 11 11
%e 100 1TT, 100
%e 101 1T0, 1T1, 10T, 101
%e 110 11T, 110
%e 111 111
%e 1000 1TTT, 1000
%e 1001 1TT0, 1TT1, 100T, 1001
%e 1010 1T0T, 1T01, 1T1T, 1T10, 10T0, 10T1, 101T, 1010
%e 1011 1T00, 1T11, 10TT, 1011
%e 1100 11TT, 1100
%e 1101 11T0, 11T1, 110T, 1101
%e 1110 111T, 1110
%e 1111 1111
%o (PARI) \\ See Links section.
%Y See A371257 for a similar sequence.
%Y Cf. A225081, A371266 (inverse).
%K nonn,base,tabf
%O 0,3
%A _Rémy Sigrist_, Mar 16 2024
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