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A372031
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(2*n+2) = a(2*n+1) * a(n+1).
2
1, 2, 3, 6, 4, 12, 5, 30, 7, 28, 8, 96, 9, 45, 10, 300, 11, 77, 13, 364, 14, 112, 15, 1440, 16, 144, 17, 765, 18, 180, 19, 5700, 20, 220, 21, 1617, 22, 286, 23, 8372, 24, 336, 25, 2800, 26, 390, 27, 38880, 29, 464, 31, 4464, 32, 544, 33, 25245, 34, 612, 35
OFFSET
1,2
COMMENTS
Conjecture: this sequence is a permutation of the positive integers.
For any prime number p, the first multiple of p in the sequence is precisely p.
LINKS
Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A007814(n), the 2-adic valuation of n)
Rémy Sigrist, PARI program
EXAMPLE
The first terms, arranged alongside a binary tree where each right child equals its parent times its sibling, are:
|
1
|
.-------2-------.
| |
.---3---. .---6---.
| | | |
.-4-. .12-. .-5-. .30-.
| | | | | | | |
7 28 8 96 9 45 10 300
PROG
(PARI) \\ See Links section.
CROSSREFS
See A372030 for similar sequences.
Cf. A007814.
Sequence in context: A302848 A046202 A372127 * A225642 A273317 A328443
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 16 2024
STATUS
approved