A362947 - OEIS

%I #14 Jul 06 2023 08:55:52

%S 0,0,1,2,1,2,3,1,1,1,2,4,1,1,3,2,2,2,3,3,1,3,4,1,4,5,1,1,4,6,1,4,7,1,

%T 1,5,2,1,5,3,1,5,4,2,2,8,1,3,6,1,5,5,1,6,6,1,7,2,1,6,8,1,4,9,2,2,10,3,

%U 1,7,3,1,8,5,1,7,4,2,6,2,3,9,1,2,7,2,3,10,2,4,7,3,2,11,1,1,6,12

%N a(0) = 0, a(1) = 0; for n > 1, a(n) is the number of pairs of consecutive terms whose product has same value as a(n-2) * a(n-1).

%C Similarly to A364027 the same number cannot occur four times in a row. In the first 10 million terms three consecutive equal numbers occurs twenty-three times, the last such triplet being a(8247993)..a(8247995) = 59. It is likely such triplets occur infinitely often although this is unknown.

%H Scott R. Shannon, <a href="/A362947/b362947.txt">Table of n, a(n) for n = 0..10000</a>.

%H Scott R. Shannon, <a href="/A362947/a362947.png">Image of the first 10 million terms</a>.

%e a(2) = 1 as there is one pair whose product equals a(0) * a(1) = 0, namely a(0) * a(1).

%e a(3) = 2 as a(1) * a(2) = 0 * 1 = 0, and there has been two previous pairs whose product is 0, namely a(0) * a(1) and a(1) * a(2).

%e a(11) = 4 as a(9) * a(10) = 1 * 2 = 2, and there has been four previous pairs whose product is 2, namely a(2) * a(3), a(3) * a(4), a(4) * a(5) and a(9) * a(10).

%Y Cf. A364027, A364036, A342585, A347062.

%K nonn

%O 0,4

%A _Scott R. Shannon_, Jul 05 2023