A377543 a(n) = least prime > a(n - 1)*a(n - 3)/a(n - 2), with a(1) = 2, a(2) = 3, a(3) = 5.

2, 3, 5, 5, 5, 7, 11, 11, 11, 13, 17, 17, 17, 19, 23, 23, 23, 29, 31, 29, 29, 37, 41, 37, 37, 43, 47, 41, 41, 53, 59, 47, 43, 59, 67, 53, 47, 61, 71, 59, 53, 67, 79, 67, 59, 71, 83, 71, 61, 73, 89, 79, 67, 79, 97, 83, 71, 83, 101, 89, 79, 97, 113, 97, 89

Offset

1,1

Comments

As (a(n)) is not monotonic, a natural question is this: if the recurrence is changed to "least prime such that b(n) > r*b(n - 1)*b(n - 3)/b(n - 2)", then what is the least r such that (b(n)) is strictly increasing? See A377544.

Links

Table of n, a(n) for n=1..65.

Mathematica

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

Crossrefs

Cf. A000040, A377544.

Sequence in context: A246401 A003660 A065688 * A348976 A169787 A165959

Adjacent sequences: A377540 A377541 A377542 * A377544 A377545 A377546

Keyword

nonn,new

Author

Clark Kimberling, Nov 13 2024

Status

approved