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A326927
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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}.
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1
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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, 45, 10, 98, 22, 50, 14, 63, 35, 125, 65, 52, 39, 147, 51, 68, 85, 153, 34, 242, 26, 117, 81, 99, 77, 175, 49, 5, 60, 80, 64, 112, 140, 105, 135, 30, 40, 32, 56, 42, 54
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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.
Unlike A316667, this sequence is infinite.
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LINKS
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Table of n, a(n) for n=1..65.
Rémy Sigrist, PARI program for A326927
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FORMULA
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n and A001222(a(n)) have opposite parity.
Odd-indexed terms belong to A028260, even-indexed terms belong to A026424.
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EXAMPLE
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The first terms, alongside a(n+1)/a(n), are:
n a(n) a(n+1)/a(n)
-- ---- -----------
1 1 2^+2 * 3^+1
2 12 2^-2 * 3^+1
3 9 2^+1 * 3^-2
4 2 2^+2 * 3^+1
5 24 2^-2 * 3^+1
6 18 2^+1 * 3^-2
7 4 2^-2 * 3^+1
8 3 3^-1 * 5^+2
9 25 5^-2 * 7^+1
10 7 2^+2 * 3^+1
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PROG
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(PARI) See Links section.
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CROSSREFS
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Cf. A001222, A026424, A028260, A309817, A316667.
Sequence in context: A038334 A101501 A299515 * A338289 A018870 A327470
Adjacent sequences: A326924 A326925 A326926 * A326928 A326929 A326930
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KEYWORD
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nonn
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AUTHOR
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Rémy Sigrist, Oct 22 2019
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STATUS
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approved
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