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A337327 Maximum value of the cyclic self convolution of the first n terms of the characteristic function of primes. 2
0, 1, 2, 2, 3, 2, 4, 3, 3, 3, 4, 4, 6, 5, 4, 4, 6, 5, 8, 7, 6, 6, 8, 7, 8, 7, 6, 6, 8, 7, 10, 9, 8, 8, 8, 8, 10, 9, 8, 8, 10, 10, 12, 12, 10, 11, 12, 12, 12, 13, 12, 12, 14, 13, 14, 13, 12, 12, 12, 12, 14, 13, 12, 13, 12, 14, 14, 15, 12, 14, 14, 16, 16, 18 (list; graph; refs; listen; history; text; internal format)
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 here 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

Cf. A010051, A299111, A014342.

Sequence in context: A163870 A327664 A155043 * A065770 A297113 A086375

Adjacent sequences:  A337324 A337325 A337326 * A337328 A337329 A337330

KEYWORD

nonn,look

AUTHOR

Andres Cicuttin, Aug 23 2020

STATUS

approved

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Last modified January 25 14:42 EST 2021. Contains 340416 sequences. (Running on oeis4.)