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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 (list; graph; refs; listen; history; text; internal format)



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.


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

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


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.


Cf. A000945, A000946.

Sequence in context: A080376 A005669 A038664 * A148077 A148078 A093156

Adjacent sequences:  A261364 A261365 A261366 * A261368 A261369 A261370




Sean A. Irvine, Aug 16 2015



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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)