A340730 a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-1) - min(a(n-1),n) if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + min(a(n-1),n).

0, 1, 2, 4, 8, 3, 6, 12, 20, 11, 21, 10, 20, 7, 14, 28, 44, 27, 9, 18, 36, 15, 30, 53, 29, 54, 80, 107, 79, 50, 80, 49, 17, 34, 68, 33, 66, 103, 65, 26, 52, 93, 51, 94, 138, 183, 137, 90, 42, 84, 134, 83, 31, 62, 116, 61, 5, 10, 20, 40, 80, 19, 38, 76, 140, 75, 141, 74, 142, 73, 143, 72, 144

Offset: 0

Author

Scott R. Shannon, Jan 17 2021

Keywords

• nonn

Comments

This sequence uses the same rules as Recamán's sequence A005132 except that the step size for each term n is set to the minimum of n and a(n-1).

The terms are slightly concentrated along the linear relationships a(n) = k*n, where k is an integer >= 1. Other values are distributed between these lines. See the linked image.

The smallest value not to have appeared after 5 million terms is 8697. It is unknown if all terms eventually appear.

Examples

			a(3) = 4 as min(3,a(2)) = min(3,2) = 2, and as 0 has already appeared a(3) = a(2) + 2 = 2 + 2 = 4.
a(5) = 3 as min(5,a(4)) = min(5,8) = 5, and as 3 has not already appeared a(5) = a(4) - 5 = 8 - 5 = 3.
		

Links

• Scott R. Shannon, Image of the first 5 million terms.

Crossrefs

Cf. A005132, A336760, A336761.