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

1,2

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.

Links

Table of n, a(n) for n=1..54.

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

Adjacent sequences: A371356 A371357 A371358 * A371360 A371361 A371362

Keyword

nonn

Author

Neal Gersh Tolunsky, Mar 19 2024

Extensions

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

Status

approved