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