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A371359
a(1)=1; for n>1, a(n) = a(n-1) / k if there exists an unused positive integer k (choose the smallest) such that a(n) is a distinct positive integer; otherwise a(n) = a(n-1) * k if the same conditions apply.
1
1, 2, 6, 24, 4, 20, 140, 14, 112, 8, 72, 3, 33, 396, 22, 286, 13, 195, 5, 80, 1360, 68, 1292, 38, 798, 21, 483, 7, 175, 4550, 130, 3510, 117, 3276, 91, 2639, 29, 899, 28768, 496, 16368, 372, 13764, 222, 8880, 185, 7585, 41, 1722, 74046, 903, 40635, 645, 29670
OFFSET
1,2
COMMENTS
A sequence of distinct positive integers in which the ratios of successive terms (larger over smaller) are all distinct.
A100707 is an analogous sequence using addition and subtraction.
EXAMPLE
a(1)=1: 1 * 2 = 2 (k=2 is the smallest number not yet used as a divisor or multiplier).
a(2)=2: 2 * 3 = 6 (k=3 has not been used before).
a(3)=6: 6 * 4 = 24 (k=4 has not been used before).
a(4)=24: 24 / 6 = 4 (k=6 has not been used before).
a(11)=72: 72 / 24 = 3 (k=24 has not been used before). Note that we would have used k=12 if this did not result in a repeated term (72 / 12 = a(3)=6).
CROSSREFS
Cf. A100707, A371360 (k values).
Sequence in context: A007672 A322255 A084337 * A323615 A204934 A033642
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Mar 19 2024
EXTENSIONS
a(12) and beyond from John Tyler Rascoe, Mar 20 2024
STATUS
approved