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A261367
Number of nodes at level n in Euclid-Mullin graph starting with 1.
0
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
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
Sequence in context: A080376 A005669 A038664 * A148077 A148078 A093156
KEYWORD
nonn,hard,more
AUTHOR
Sean A. Irvine, Aug 16 2015
STATUS
approved