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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.
2
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.
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
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Mar 13 2019
STATUS
approved