A362947 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).

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, 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, 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

Offset: 0

Author

Scott R. Shannon, Jul 05 2023

Keywords

• nonn

Comments

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.

Examples

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

Links

• Scott R. Shannon, Table of n, a(n) for n = 0..10000.
• Scott R. Shannon, Image of the first 10 million terms.

Crossrefs

Cf. A364027, A364036, A342585, A347062.