A261367 Number of nodes at level n in Euclid-Mullin graph starting with 1.

1, 1, 1, 1, 1, 2, 4, 9, 24, 52, 165, 555, 2020

Offset

0,6

Comments

The Euclid-Mullin graph encodes all instances of Euclid's proof of the infinitude of primes. This sequences gives the number of nodes appearing at each level in the graph, when starting the graph from 1.

a(13) is almost certainly 7950 but requires the factorization of a 253-digit number to confirm.

Links

Table of n, a(n) for n=0..12.

Andrew R. Booker and Sean A. Irvine, The Euclid-Mullin Graph, to appear (2015).

Example

Level 0 contains the single node 1, so a(0)=1.
Level 1 contains the prime factors of 1+1, i.e., 2, so a(1)=2.
The first interesting level is Level 5, which has the factors of 1*2*3*7*43+1 which are 13 and 139, hence a(5)=2.
At higher levels there can be more than one path from a node back to the root.

Crossrefs

Cf. A000945, A000946.

Sequence in context: A080376 A005669 A038664 * A148077 A148078 A093156

Adjacent sequences: A261364 A261365 A261366 * A261368 A261369 A261370

Keyword

nonn,hard,more

Author

Sean A. Irvine, Aug 16 2015

Status

approved