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%I #27 Jan 14 2018 14:03:11
%S 1,2,4,3,8,6,12,5,9,16,24,10,18,20,36,7,32,15,48,28,40,60,72,14,56,30,
%T 96,44,64,84,120,11,42,80,144,21,54,168,192,52,108,88,216,132,156,240,
%U 264,22,66,104,288,78,90,312,336,68,180,112,360,204,228,384
%N Lexicographically earliest sequence of distinct positive terms such that, for any n > 1 with binary expansion (b_1, b_2, ..., b_k) (where b_1 = 1 is the most significant bit of n), a(n) is a multiple of a(i) for each i such that b_i = 1.
%C This sequence is a permutation of the natural numbers, with inverse A297499; as a(1) = 1, for any k > 1, a(2^k) has only to be a multiple of 1, and so a(2^k) will be the least unused value, and eventually any number will appear in the sequence.
%C Prime numbers can only appear at positions that are powers of 2.
%C For any n > 1, a(n) is a multiple of m(n) = lcm(a(e_1), ..., a(e_h)) where the list (e_1, ..., e_h) corresponds to the ones in the binary expansion of n (in particular, e_1 = 1 and h = A000120(n)); the lines and dashed lines visible in the logarithmic scatterplot of the first terms correspond to sets of terms a(n) where m(n) has the same value (see Links section).
%H Rémy Sigrist, <a href="/A295029/b295029.txt">Table of n, a(n) for n = 1..50000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H Rémy Sigrist, <a href="/A295029/a295029.png">Colored logarithmic scatterplot of the first 150000 terms</a> (where the color is function of m(n))
%H Rémy Sigrist, <a href="/A295029/a295029.gp.txt">PARI program for A295029</a>
%e The first terms, alongside the binary expansion of n and m(n), are:
%e n a(n) bin(n) m(n)
%e -- ---- ------ -------------
%e 1 1 1 1 = lcm(a(1))
%e 2 2 10 1 = lcm(a(1))
%e 3 4 11 2 = lcm(a(1), a(2))
%e 4 3 100 1 = lcm(a(1))
%e 5 8 101 4 = lcm(a(1), a(3))
%e 6 6 110 2 = lcm(a(1), a(2))
%e 7 12 111 4 = lcm(a(1), a(2), a(3))
%e 8 5 1000 1 = lcm(a(1))
%e 9 9 1001 3 = lcm(a(1), a(4))
%e 10 16 1010 4 = lcm(a(1), a(3))
%e 11 24 1011 12 = lcm(a(1), a(3), a(4))
%e 12 10 1100 2 = lcm(a(1), a(2))
%e 13 18 1101 6 = lcm(a(1), a(2), a(4))
%e 14 20 1110 4 = lcm(a(1), a(2), a(3))
%e 15 36 1111 12 = lcm(a(1), a(2), a(3), a(4))
%e 16 7 10000 1 = lcm(a(1))
%e 17 32 10001 8 = lcm(a(1), a(5))
%e 18 15 10010 3 = lcm(a(1), a(4))
%e 19 48 10011 24 = lcm(a(1), a(4), a(5))
%e 20 28 10100 4 = lcm(a(1), a(3))
%o (PARI) See Links section.
%Y Cf. A000120, A297499 (inverse).
%K nonn,base
%O 1,2
%A _Rémy Sigrist_, Dec 30 2017
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