OFFSET

1,3

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Andres Cicuttin, Graph of first 2^10 terms

EXAMPLE

The primes among the first 5 positive integers (1,2,3,4,5) are 2, 3, and 5, then the corresponding characteristic function of primes is (0,1,1,0,1) (see A010051) and the corresponding five possible cyclic self-convolutions are the dot products between (0,1,1,0,1) and the rotations of its mirrored version as shown below:

(0,1,1,0,1).(1,0,1,1,0) = 0*1 + 1*0 + 1*1 + 0*1 + 1*0 = 1,

(0,1,1,0,1).(0,1,0,1,1) = 0*0 + 1*1 + 1*0 + 0*1 + 1*1 = 2,

(0,1,1,0,1).(1,0,1,0,1) = 0*1 + 1*0 + 1*1 + 0*0 + 1*1 = 2,

(0,1,1,0,1).(1,1,0,1,0) = 0*1 + 1*1 + 1*0 + 0*1 + 1*0 = 1,

(0,1,1,0,1).(0,1,1,0,1) = 0*0 + 1*1 + 1*1 + 0*0 + 1*1 = 3.

Then a(5)=3 because 3 is the maximum among the five values.

MATHEMATICA

b[n_]:=Table[If[PrimeQ[i], 1, 0], {i, 1, n}];

Table[Max@Table[b[n].RotateRight[Reverse[b[n]], j], {j, 0, n-1}], {n, 1, 100}]

PROG

(PARI) a(n) = vecmax(vector(n, k, sum(i=1, n, isprime(n-i+1)*isprime(1+(i+k)%n)))); \\ Michel Marcus, Aug 26 2020

CROSSREFS

KEYWORD

nonn,look

AUTHOR

Andres Cicuttin, Aug 23 2020

STATUS

approved