cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A347404 a(1) = 3; for n > 2, a(n) is the smallest distinct positive integer such that gcd(a(n), a(n-k)) > 1 for each divisor k of a(n) such that k < n.

Original entry on oeis.org

3, 6, 9, 12, 15, 18, 10, 2, 14, 4, 22, 8, 24, 16, 20, 28, 26, 30, 34, 32, 36, 40, 5, 50, 60, 38, 42, 44, 46, 48, 54, 52, 58, 56, 62, 64, 66, 68, 70, 72, 74, 78, 39, 90, 57, 21, 51, 69, 84, 87, 33, 27, 96, 81, 63, 7, 126, 45, 168, 99, 93, 75, 95, 19, 114, 105, 77, 198, 153, 165, 11, 132, 55, 595
Offset: 1

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Author

Scott R. Shannon, Aug 30 2021

Keywords

Comments

The majority of terms are concentrated along a line whose slope is approximately 1.3. Occasionally though there are terms which correspond to the smallest unused number up to that point, and these tend to lead to a subsequent very large term. For example a(499) = 628, a(500) = 682, a(501) = 31, a(502) = 14322. Other large terms appear seemingly at random, for example a(15449) = 19880, a(15450) = 19099, a(15451) = 74962230.
It is likely all numbers > 1 eventually appear. The smallest number not seen after 20000 terms is 89.
Note that if the sequence starts with 2 then the terms are just all the increasing even numbers.

Examples

			a(2) = 6. As a(1) = 3 the next term must be a multiple of 3, and the smallest unused such number is 6. Note that as a(2-2), a(2-3) and a(2-6) are not defined these are ignored.
a(7) = 10. As a(6) = 18 the next term must have 2 and/or 3 as divisors. If it has 2 as a divisor is must also have 3 and/or 5 as a divisor as a(8-2) = a(6) = 15. The smallest unused number satisfying these is 10. Note that as 5 is a divisor of 10 it must be that a(7-5) = a(2) = 6 has 2 or 5 as a divisor, which is true.
a(8) = 2. As a(7) = 10 the next term must have 2 and/or 5 as a divisor. As a(6) = 18 also has 2 as a divisor a(8) = 2 is the next smallest unused term.
		

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