A051614 4th term in Euclid-Mullin prime sequence started with n-th prime (cf. A000945).

43, 43, 3, 43, 3, 79, 3, 5, 3, 3, 11, 223, 3, 7, 3, 3, 827, 367, 13, 3, 439, 5, 3, 3, 11, 5, 619, 3, 5, 3, 7, 3, 3, 5, 5, 907, 23, 11, 3, 3, 3, 1087, 3, 19, 3, 5, 7, 13, 3, 5, 3, 3, 1447, 3, 3, 3, 3767, 1627, 1663, 3, 1699, 3, 19, 5, 1879, 3, 1987, 7, 3, 5, 4943, 3, 2203, 2239, 5, 23

Offset

1,1

Comments

First term in Euclid-Mullin sequence is p(n) (say), 2nd term (if p(n) odd) is 2, 3rd term is A094460(n). Further terms are respectively A094461(n), A094462(n), and A094463(n). [Comment rewritten by Jianing Song, Dec 29 2025]

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

E.g., (5,2,11,3), (89,2,179,3), (17,2,5,3), (2,3,7,43), (61,2,3,367).

Mathematica

a[n_] := (Clear[f]; f[1] = Prime[n]; f[k_] := f[k] = FactorInteger[Product[f[i], {i, 1, k-1}]+1][[1, 1]]; f[4]); Table[a[n], {n, 1, 76}] (* Jean-François Alcover, Feb 05 2014 *)

Crossrefs

Cf. A000945, A000040, A005384, A005385, A023592, A051308 - A051335.

Sequence in context: A127147 A298078 A291494 * A291479 A259089 A165864

Adjacent sequences: A051611 A051612 A051613 * A051615 A051616 A051617

Keyword

nonn,easy,nice

Author

Labos Elemer

Status

approved