A346270 Number of distinct solutions for the maximum value of the Gilbreath equation of an ordered sequence of n integers.

1, 1, 2, 6, 32, 270, 4512, 141816

Offset

1,3

Links

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

Riccardo Gatti, Gilbreath Sequences and Proof of Conditions for Gilbreath Conjecture, Preprints 2020, 2020030145.

Riccardo Gatti, Program for the generation of the sequence calling int Gen(int n) function

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

Sequence in context: A012324 A121676 A326096 * A133596 A088437 A191691

Adjacent sequences: A346267 A346268 A346269 * A346271 A346272 A346273

Keyword

nonn,hard,more

Author

Riccardo Gatti, Jul 12 2021

Extensions

a(8) from Riccardo Gatti, Aug 29 2021

Status

approved