cp's OEIS Frontend

A354749 a(1) = 1; for n > 1, a(n) is the smallest positive number greater than 1 that is coprime to a(n-1) and the product a(n) * a(n-1) is distinct from all previous products a(i) * a(i-1), i=2..n-1.

%I A354749 #19 Jun 13 2022 08:45:33
%S A354749 1,2,3,4,5,2,7,3,5,6,7,4,9,2,11,3,8,5,7,8,9,5,11,4,13,2,17,3,13,5,12,
%T A354749 7,9,10,7,11,6,13,7,15,8,11,9,13,8,17,4,19,2,23,3,16,5,17,6,19,3,25,2,
%U A354749 27,4,23,5,19,7,16,9,14,11,10,13,11,12,13,14,15,11,16,13,15,16,17,7,20,9
%N A354749 a(1) = 1; for n > 1, a(n) is the smallest positive number greater than 1 that is coprime to a(n-1) and the product a(n) * a(n-1) is distinct from all previous products a(i) * a(i-1), i=2..n-1.
%C A354749 This is a variation of A354803 where all terms beyond the first must be greater than 1. In the first 1000000 terms the fixed points are 1,2,3,4,5,7, it is likely no more exist, while the smallest number not to have appeared is 2090. The sequence is conjectured to be a permutation of the positive integers.
%C A354749 See A354759 for the products of all pairs of terms.
%H A354749 Scott R. Shannon, <a href="/A354749/a354749.png">Image of the first 500000 terms</a>.
%e A354749 a(6) = 2 as a(5) = 5 and 2 is the smallest number greater than 1 that is coprime to 5 and whose product with 5, 2 * 5 = 10, has not previously appeared.
%Y A354749 Cf. A354759, A354803, A354804, A354753, A354754, A088177.
%K A354749 nonn,look
%O A354749 1,2
%A A354749 _Scott R. Shannon_, Jun 06 2022