A332553 a(n) = n + A082183(n) - A082184(n).

1, 2, 3, 2, 3, 6, 5, 3, 5, 7, 8, 6, 4, 10, 15, 8, 9, 14, 5, 7, 11, 15, 9, 12, 8, 6, 21, 14, 15, 30, 21, 11, 17, 7, 24, 18, 12, 15, 32, 20, 21, 32, 8, 15, 23, 31, 27, 14, 16, 12, 39, 26, 9, 15, 32, 19, 29, 39, 40, 30, 20, 42, 51, 10, 33, 50, 17, 23, 35

Offset: 2

Author

N. J. A. Sloane, Feb 21 2020, at the suggestion of Bradley Klee

Keywords

• nonn

Comments

Since (by definition) a(n) = n + A082183(n) - A082184(n) = - (n^2 + A082183(n)^2 - A082184(n)^2), this can be described as the distance of (n, A082183(n), A082184(n)) from a Pythagorean triple. Also a(n) > 0 for all n. See the Myers et al. link. - Bradley Klee, Feb 19 2020

Comments from N. J. A. Sloane, Feb 23 2020: (Start)

To study the lowest values taken by a(n), consider the record high values of n/a(n). The data suggests two conjectures.

Conjecture 1: The record high values of n/a(n) are j/2 + 1 for j = 2,3,4,5,... and occur at n = j*(j+1)/2 - 1.

This would imply:

Conjecture 2: Let j = 2,3,4,5,... For 1 <= n < T_j - 1, a(n) > 2*n/(j+2). (End)

Links

• N. J. A. Sloane, Table of n, a(n) for n = 2..1000
• J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000, April 2020.

Crossrefs

Cf. A082183, A082184, A332552.