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

Author

Rémy Sigrist, Mar 13 2019

Keywords

• nonn
• look

Comments

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

Examples

			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)
		

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

Crossrefs

Cf. A064547, A285487, A306856 (inverse).

Programs

PARI

See Links section.

Formula

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