OFFSET
1,3
LINKS
Riccardo Gatti, Gilbreath Sequences and Proof of Conditions for Gilbreath Conjecture, Preprints 2020, 2020030145.
A. M. Odlyzko, Iterated absolute values of differences of consecutive primes, Mathematics of computation, 61 (1993), 373-380.
EXAMPLE
For n=1, let the ordered sequence of integers be S = (s_1). The maximum value of the Gilbreath equation of S is k = s_1 + 1. Rewriting this as a function of s_1 gives s_1 + 1, which can take only 1 value, so a(1)=1.
For n=2, let the ordered sequence of integers be S = (s_1, s_2). The maximum value of the Gilbreath equation of S is k = s_1^1 + s2 + 1. Rewriting this as a function of s_1, s_2 gives 1 - s_1 + 2*s_2, which can take only 1 value, so a(2)=1.
For n=3, let the ordered sequence of integers be S = (s_1, s_2, s_3). The maximum value of the Gilbreath equation of S is k = s_1^2 + s_2^1 + s_3 + 1. Rewriting this as a function of s_1, s_2, s_3 gives 1 - s_2 + 2*s_3 + |s_1 - 2*s_2 + s_3|, which can take 2 distinct values, so a(3)=2.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Riccardo Gatti, Jul 12 2021
EXTENSIONS
a(8) from Riccardo Gatti, Aug 29 2021
STATUS
approved