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

1,2

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A298480

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.

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A317490 A256466 A303771 * A353916 A370501 A253279

Adjacent sequences: A298477 A298478 A298479 * A298481 A298482 A298483

Keyword

nonn

Author

Rémy Sigrist, Jul 21 2018

Status

approved