A298480 Lexicographically earliest sequence of distinct positive terms such that the Fermi-Dirac factorizations of two consecutive terms differ by exactly one factor.

1, 2, 6, 3, 12, 4, 8, 24, 120, 30, 10, 5, 15, 60, 20, 40, 280, 56, 14, 7, 21, 42, 168, 84, 28, 140, 35, 70, 210, 105, 420, 840, 7560, 1080, 216, 54, 18, 9, 27, 108, 36, 72, 360, 90, 45, 135, 270, 1890, 378, 126, 63, 189, 756, 252, 504, 1512, 16632, 1848, 264

Offset: 1

Author

Rémy Sigrist, Jul 21 2018

Keywords

• nonn

Comments

For Fermi-Dirac representation of n see A182979. - N. J. A. Sloane, Jul 21 2018

For any n > 0, either a(n)/a(n+1) or a(n+1)/a(n) belongs to A050376.

This sequence has similarities with A282291; in both sequences, each pair of consecutive terms contains a term that divides the other.

Examples

			The first terms, alongside a(n+1)/a(n), are:
  n   a(n)  a(n+1)/a(n)
  --  ----  -----------
   1     1        2
   2     2        3
   3     6      1/2
   4     3        2^2
   5    12      1/3
   6     4        2
   7     8        3
   8    24        5
   9   120      1/2^2
  10    30      1/3
  11    10      1/2
  12     5        3
  13    15        2^2
  14    60      1/3
  15    20        2
  16    40        7
  17   280      1/5
  18    56      1/2^2
  19    14      1/2
  20     7        3
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A298480

Crossrefs

Cf. A000120, A050376, A052330, A052331, A282291, A182979.

Programs

PARI

See Links section.

Formula

A000120(A052331(a(n)) XOR A052331(a(n+1))) = 1 for any n > 0 (where XOR denotes the bitwise XOR operator).

Apparently, a(n) = A052330(A163252(n-1)) for any n > 0.