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, 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.

Links

Table of n, a(n) for n=1..65.

Rémy Sigrist, PARI program for A326927

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

Cf. A001222, A026424, A028260, A309817, A316667.

Sequence in context: A038334 A101501 A299515 * A338289 A018870 A327470

Adjacent sequences: A326924 A326925 A326926 * A326928 A326929 A326930

Keyword

nonn

Author

Rémy Sigrist, Oct 22 2019

Status

approved