A371216 a(0) = 1, a(1) = 1; for n >= 2, a(n) = Min(a(n - 1), a(n - 2)) + GCD(a(n - 1), n - 1).

1, 1, 2, 3, 5, 4, 5, 5, 6, 7, 7, 8, 8, 12, 9, 10, 14, 12, 13, 13, 14, 15, 17, 16, 17, 17, 18, 19, 19, 20, 20, 30, 21, 22, 32, 24, 25, 25, 26, 27, 29, 28, 29, 29, 30, 31, 31, 32, 32, 48, 33, 34, 50, 36, 37, 37, 38, 39, 41, 40, 41, 41, 42, 43, 43, 44, 44, 66, 45, 46, 68

Offset

0,3

Comments

The plots of a(n) and a(n) - a(n-1) are interesting. Empirically 2*n/3 <= a(n) <= (n-1) and 2/3 <= a(n)/a(n-1) <= 3/2.

Links

Table of n, a(n) for n=0..70.

Example

a(0) = 1;
a(1) = 1;
a(2) = Min(1, 1) + GCD(1, 1) = 2;
a(3) = Min(2, 1) + GCD(2, 2) = 3;
a(4) = Min(3, 2) + GCD(3, 3) = 5;
and so on.

Mathematica

a[0] = a[1] = 1; a[n_] := a[n] = Min[a[n - 1], a[n - 2]] + GCD[a[n - 1], n - 1]; Array[a, 100, 0] (* Amiram Eldar, Mar 15 2024 *)

Crossrefs

Cf. A364918.

Sequence in context: A321782 A104204 A131296 * A267808 A239852 A263279

Adjacent sequences: A371213 A371214 A371215 * A371217 A371218 A371219

Keyword

nonn

Author

Ctibor O. Zizka, Mar 15 2024

Status

approved