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A299111 Maximum value of the cyclic convolution of first n primes with themselves. 3
4, 13, 37, 82, 183, 344, 601, 918, 1355, 2048, 2873, 3978, 5455, 7112, 9105, 11530, 14391, 17504, 21353, 25686, 30311, 35536, 41421, 48010, 55911, 64632, 73869, 83766, 94151, 105420, 118569, 132566, 148247, 164564, 182617, 201770, 222975, 245532, 269253 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 2000 terms from Robert Israel)

FORMULA

a(n) = Max_{k=1..n} Sum_{i=1..n} prime(n-i+1)*prime(1+(i+k) mod n).

a(n) >= A014342(n). Does the ratio a(n)/A014342(n) have a limit as n -> infinity? - Robert Israel, Feb 07 2018

EXAMPLE

For n = 4 the four possible cyclic convolution of first four primes with themselves are:

(2,3,5,7).(7,5,3,2) = 2*7 + 3*5 + 5*3 + 7*2 = 14 + 15 + 15 + 14 = 58,

(2,3,5,7).(2,7,5,3) = 2*2 + 3*7 + 5*5 + 7*3 = 4 + 21 + 25 + 21 = 71,

(2,3,5,7).(3,2,7,5) = 2*3 + 3*2 + 5*7 + 7*5 = 6 + 6 + 35 + 35 = 82,

(2,3,5,7).(5,3,2,7) = 2*5 + 3*3 + 5*2 + 7*7 = 10 + 9 + 10 + 49 = 78,

then a(4)=82 because 82 is the maximum among the four values.

MAPLE

f:= proc(n) local V, R, i;

    V:= Vector(n, ithprime);

    R:= ArrayTools:-FlipDimension(V, 1)^%T;

    max(seq(ArrayTools:-CircularShift(R, i) . V, i=0..n-1))

end proc:

map(f, [$1..100]); # Robert Israel, Feb 07 2018

MATHEMATICA

a[n_]:=Prime[Range[n]];

Table[Max@Table[a[n].RotateRight[Reverse[a[n]], j], {j, 0, n - 1}], {n, 1, 36}]

PROG

(PARI) a(n) = vecmax(vector(n, k, sum(i=1, n, prime(n-i+1)*prime(1+(i+k)%n)))); \\ Michel Marcus, Feb 07 2018

CROSSREFS

Cf. A014342, A299053.

Sequence in context: A003727 A103082 A279111 * A324250 A226866 A048474

Adjacent sequences:  A299108 A299109 A299110 * A299112 A299113 A299114

KEYWORD

nonn

AUTHOR

Andres Cicuttin, Feb 02 2018

STATUS

approved

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Last modified April 20 04:42 EDT 2019. Contains 322294 sequences. (Running on oeis4.)