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
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
Programs
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PARI
See Links section.
Formula
A064547(a(n) * a(n+1)) >= 5.
Comments