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%I #16 Dec 11 2019 02:35:22
%S 1,12,9,2,24,18,4,3,25,7,84,48,36,8,6,27,15,20,16,28,21,75,33,44,55,
%T 45,10,98,22,50,14,63,35,125,65,52,39,147,51,68,85,153,34,242,26,117,
%U 81,99,77,175,49,5,60,80,64,112,140,105,135,30,40,32,56,42,54
%N Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(n+1)/a(n) = p^x * q^y where p and q are two distinct prime numbers and {abs(x), abs(y)} = {1, 2}.
%C This sequence can be seen as a variant of the knight's tour described in A316667 transposed to the space with infinite dimensions described in A309817; two positions in N^N are at knight's distance if they differ exactly by 2 units alongside some axis and by 1 unit alongside some other axis.
%C Unlike A316667, this sequence is infinite.
%H Rémy Sigrist, <a href="/A326927/a326927.gp.txt">PARI program for A326927</a>
%F n and A001222(a(n)) have opposite parity.
%F Odd-indexed terms belong to A028260, even-indexed terms belong to A026424.
%e The first terms, alongside a(n+1)/a(n), are:
%e n a(n) a(n+1)/a(n)
%e -- ---- -----------
%e 1 1 2^+2 * 3^+1
%e 2 12 2^-2 * 3^+1
%e 3 9 2^+1 * 3^-2
%e 4 2 2^+2 * 3^+1
%e 5 24 2^-2 * 3^+1
%e 6 18 2^+1 * 3^-2
%e 7 4 2^-2 * 3^+1
%e 8 3 3^-1 * 5^+2
%e 9 25 5^-2 * 7^+1
%e 10 7 2^+2 * 3^+1
%o (PARI) See Links section.
%Y Cf. A001222, A026424, A028260, A309817, A316667.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Oct 22 2019
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