cp's OEIS Frontend

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.

%I A371359 #36 Jan 05 2025 01:30:03
%S A371359 1,2,6,24,4,20,140,14,112,8,72,3,33,396,22,286,13,195,5,80,1360,68,
%T A371359 1292,38,798,21,483,7,175,4550,130,3510,117,3276,91,2639,29,899,28768,
%U A371359 496,16368,372,13764,222,8880,185,7585,41,1722,74046,903,40635,645,29670
%N 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.
%C A371359 A sequence of distinct positive integers in which the ratios of successive terms (larger over smaller) are all distinct.
%C A371359 A100707 is an analogous sequence using addition and subtraction.
%H A371359 Neal Gersh Tolunsky, <a href="/A371359/b371359.txt">Table of n, a(n) for n = 1..10000</a>
%e A371359 a(1)=1: 1 * 2 = 2 (k=2 is the smallest number not yet used as a divisor or multiplier).
%e A371359 a(2)=2: 2 * 3 = 6 (k=3 has not been used before).
%e A371359 a(3)=6: 6 * 4 = 24 (k=4 has not been used before).
%e A371359 a(4)=24: 24 / 6 = 4 (k=6 has not been used before).
%e A371359 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).
%Y A371359 Cf. A100707, A371360 (k values).
%K A371359 nonn
%O A371359 1,2
%A A371359 _Neal Gersh Tolunsky_, Mar 19 2024
%E A371359 a(12) and beyond from _John Tyler Rascoe_, Mar 20 2024