A224894 a(1) = 1, a(n+1) = smallest prime divisor of 1 + product of all the primes p <= a(n).

1, 2, 3, 7, 211, 1051, 91943, 206705778299

Offset

1,2

Comments

Following Euclid's proof that there are infinitely many primes.

For example, 211 is 2*3*5*7 + 1 and 1051 is the smallest prime divisor of 2*3*5*...*211 + 1. This differs from the Euclid-Mullin sequence (A000945) because all the primes between a(n-1) and a(n) are used in calculating a(n+1).

Links

Table of n, a(n) for n=1..8.

Example

a(5) = 2*3*5*7 + 1 = 211.
a(6) = 1051 because 1051 is the smallest prime divisor of 2*3*5*...*211 + 1.

Mathematica

a[1] = 1; a[n_] := a[n] =  Block[{pr = 1 + Product[Prime[k], {k, PrimePi@a[n - 1]}], p = NextPrime@a[n - 1]}, While[Mod[pr, p] > 0, p = NextPrime@p]; p]; Array[a, 7] (* Giovanni Resta, Jul 24 2013 *)

Crossrefs

Sequence in context: A087311 A053924 A130060 * A266269 A053942 A053954

Adjacent sequences: A224891 A224892 A224893 * A224895 A224896 A224897

Keyword

nonn,hard

Author

Antonio Sanso, Jul 24 2013

Extensions

a(8) from Giovanni Resta, Jul 25 2013

Status

approved