A377544 a(n) = least prime > (5/3)*a(n - 1)*a(n - 3)/a(n - 2), with a(1) = 2, a(2) = 3, a(3) = 5.

2, 3, 5, 7, 11, 17, 19, 23, 37, 53, 59, 71, 107, 149, 167, 211, 317, 419, 467, 593, 887, 1171, 1307, 1657, 2477, 3257, 3637, 4621, 6899, 9059, 10133, 12889, 19207, 25169, 28151, 35809, 53377, 69941, 78203, 99487, 148301, 194309, 217253, 276359, 411967

Offset

1,1

Comments

If the recurrence is generalized to a(n) > r*a(n - 1)*a(n - 3)/b(n - 2), then 5/3 is the least value of r for which (a(n)) is strictly increasing.

Links

Table of n, a(n) for n=1..45.

Mathematica

{a[1], a[2], a[3]} = {2, 3, 5}; r = 5/3;
a[n_] := a[n] = NextPrime[r*a[n - 1] a[n - 3]/a[n - 2]];
Table[a[n], {n, 1, 100}]

Crossrefs

Cf. A000040, A377543.

Sequence in context: A302493 A188713 A280996 * A089084 A262835 A258261

Adjacent sequences: A377541 A377542 A377543 * A377545 A377546 A377547

Keyword

nonn

Author

Clark Kimberling, Nov 13 2024

Status

approved