%I #13 Jul 04 2022 13:57:02
%S 1,2,4,3,6,8,10,5,15,20,16,12,9,24,14,7,21,28,48,18,36,32,40,30,25,50,
%T 56,42,27,44,22,11,33,66,88,54,84,112,100,75,60,80,64,72,90,96,140,63,
%U 35,70,120,45,108,128,160,105,55,110,104,78,39,52,26,13
%N Lexicographically earliest sequence of distinct positive integers such that for any n > 1, a(n) is a multiple of a(A080079(n-1)).
%C This sequence is a permutation of the positive integers with inverse A355436.
%C The construction of this sequence is similar to that of A269838.
%C This sequence can also be seen as an irregular table:
%C - with row lengths given by A011782,
%C - with initial row (1),
%C - given the first k+1 rows (with globally 2^k terms), the next row contains a multiple of a(2^k), followed by a multiple of a(2^k-1), ..., followed by a multiple of a(1).
%H Rémy Sigrist, <a href="/A355435/b355435.txt">Table of n, a(n) for n = 1..8192</a>
%H Rémy Sigrist, <a href="/A355435/a355435.gp.txt">PARI program</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(2^n) = prime(n) for any n > 0 (where prime(n) denotes the n-th prime number).
%e As an irregular table, the first rows are:
%e [1]
%e [2]
%e [4, 3]
%e [6, 8, 10, 5]
%e [15, 20, 16, 12, 9, 24, 14, 7]
%e [21, 28, 48, 18, 36, 32, 40, 30, 25, 50, 56, 42, 27, 44, 22, 11]
%e .
%e The first terms are:
%e n a(n) A080079(n-1) a(A080079(n-1))
%e -- ---- ------------ ---------------
%e 1 1 N/A N/A
%e 2 2 1 1
%e 3 4 2 2
%e 4 3 1 1
%e 5 6 4 3
%e 6 8 3 4
%e 7 10 2 2
%e 8 5 1 1
%e 9 15 8 5
%e 10 20 7 10
%e 11 16 6 8
%e 12 12 5 6
%e 13 9 4 3
%e 14 24 3 4
%e 15 14 2 2
%e 16 7 1 1
%o (PARI) See Links section.
%Y Cf. A011782, A080079, A269838, A355436 (inverse).
%K nonn,tabf
%O 1,2
%A _Rémy Sigrist_, Jul 02 2022