A057458 Number of k, 1 <= k <= n, where {k (n+1-k) + 1} is prime.

1, 2, 1, 4, 0, 6, 3, 2, 2, 8, 1, 12, 2, 2, 4, 16, 2, 10, 5, 2, 8, 14, 2, 14, 2, 8, 9, 16, 0, 20, 11, 4, 4, 14, 2, 18, 16, 8, 7, 28, 2, 32, 6, 6, 10, 24, 5, 14, 14, 8, 21, 42, 0, 22, 8, 14, 12, 22, 4, 24, 18, 14, 20, 14, 2, 44, 14, 14, 10, 34, 5, 46, 20, 4, 18, 38, 4, 38, 15, 10, 16, 46, 2

Offset

1,2

Links

Table of n, a(n) for n=1..83.

Example

For n = 7, 2*6 + 1, 4*4 + 1 and 6*2 + 1 are prime, so a(7) = 3.

Maple

A057458 := proc(n)
    a := 0 ;
    for k from 1 to n do
        if isprime(1+k*(n+1-k)) then
            a := a+1 ;
        end if;
    end do:
    a;
end proc:
seq(A057458(n), n=1..80) ; # R. J. Mathar, Jan 28 2014

Mathematica

Table[Count[Table[k(n+1-k)+1, {k, n}], _?PrimeQ], {n, 90}] (* Harvey P. Dale, Jul 22 2019 *)

Crossrefs

Sequence in context: A300721 A126707 A326305 * A291193 A291200 A326143

Adjacent sequences: A057455 A057456 A057457 * A057459 A057460 A057461

Keyword

nonn

Author

Leroy Quet, Sep 26 2000

Status

approved