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A355435 Lexicographically earliest sequence of distinct positive integers such that for any n > 1, a(n) is a multiple of a(A080079(n-1)).

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