A306854 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 5 distinct Fermi-Dirac prime factors.

1, 840, 3, 280, 9, 120, 7, 216, 5, 168, 11, 210, 4, 270, 13, 264, 15, 56, 27, 40, 21, 72, 33, 70, 12, 90, 28, 30, 36, 42, 20, 54, 35, 24, 45, 66, 52, 96, 44, 78, 55, 84, 10, 108, 14, 60, 18, 105, 8, 135, 22, 140, 6, 180, 26, 132, 32, 156, 34, 165, 38, 189, 46

Offset

1,2

Comments

This sequence is a variant of A285487. Both sequences are permutations of the natural numbers and have similar graphical features.

Links

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

OEIS Wiki, "Fermi-Dirac representation" of n

Rémy Sigrist, Colored scatterplot of the first 10000 terms (where the color is function of A064547(a(n)))

Rémy Sigrist, PARI program for A306854

Index entries for sequences that are permutations of the natural numbers

Formula

A064547(a(n) * a(n+1)) >= 5.

Example

The first terms, alongside the Fermi-Dirac factorization of a(n) * a(n+1), are:
  n   a(n)  a(n) * a(n+1)
  --  ----  -------------
   1     1  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
   2   840  2^(2^0) * 2^(2^1) * 3^(2^1) * 5^(2^0)  * 7^(2^0)
   3     3  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
   4   280  2^(2^0) * 2^(2^1) * 3^(2^1) * 5^(2^0)  * 7^(2^0)
   5     9  2^(2^0) * 2^(2^1) * 3^(2^0) * 3^(2^1)  * 5^(2^0)
   6   120  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
   7     7  2^(2^0) * 2^(2^1) * 3^(2^0) * 3^(2^1)  * 7^(2^0)
   8   216  2^(2^0) * 2^(2^1) * 3^(2^0) * 3^(2^1)  * 5^(2^0)
   9     5  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
  10   168  2^(2^0) * 2^(2^1) * 3^(2^0) * 7^(2^0)  * 11^(2^0)
  11    11  2^(2^0) * 3^(2^0) * 5^(2^0) * 7^(2^0)  * 11^(2^0)
  12   210  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)

Prog

(PARI) See Links section.

Crossrefs

Cf. A064547, A285487, A306856 (inverse).

Sequence in context: A290119 A156937 A135640 * A095119 A175742 A102793

Adjacent sequences: A306851 A306852 A306853 * A306855 A306856 A306857

Keyword

nonn,look

Author

Rémy Sigrist, Mar 13 2019

Status

approved