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, 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

Author

Neal Gersh Tolunsky, Mar 19 2024

Keywords

• nonn

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.

Examples

			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).
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A100707, A371360 (k values).

Extensions

a(12) and beyond from John Tyler Rascoe, Mar 20 2024