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A326927
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}.
1
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
OFFSET
1,2
COMMENTS
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.
FORMULA
n and A001222(a(n)) have opposite parity.
Odd-indexed terms belong to A028260, even-indexed terms belong to A026424.
EXAMPLE
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
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Oct 22 2019
STATUS
approved