A089306 Smallest prime of the form n + (n+1)+ (n+2)+...+(n+k), or 0 if no such prime exists.

3, 2, 3, 0, 5, 13, 7, 17, 19, 0, 11, 0, 13, 29, 31, 0, 17, 37, 19, 41, 43, 0, 23, 0, 0, 53, 0, 0, 29, 61, 31, 0, 67, 0, 71, 73, 37, 0, 79, 0, 41, 0, 43, 89, 0, 0, 47, 97, 0, 101, 103, 0, 53, 109, 0, 113, 0, 0, 59, 0, 61, 0, 127, 0, 131, 0, 67, 137, 139, 0, 71, 0, 73, 149, 151, 0, 0

Offset

1,1

Comments

If n is prime a(n) = n, If n is not a prime but 2n+1 is a prime then a(n) = 2n+1 else a(n) = 0, as the difference of two triangular numbers is composite if the indices differ by more than 2. r(r+1)/2 - s(s+1)/2 is composite if r-s >2.

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Maple

A089306 := proc(n)
    local k;
    if not isprime(n) and not isprime(2*n+1) then
        return 0 ;
    end if;
    for k from 0 do
        p := (k+1)*(k+2*n)/2 ;
        if isprime(p) then
            return p;
        end if;
    end do:
end proc; # R. J. Mathar, Jun 06 2013

Mathematica

a[n_] := Module[{k}, If[!PrimeQ[n] && !PrimeQ[2n+1], Return[0]]; For[k = 0, True, k++, p = (k+1)(k+2n)/2; If[PrimeQ[p], Return[p]]]];
Array[a, 100] (* Jean-François Alcover, Mar 25 2020, after R. J. Mathar *)

Crossrefs

Sequence in context: A324052 A103491 A268932 * A244996 A086099 A048967

Adjacent sequences: A089303 A089304 A089305 * A089307 A089308 A089309

Keyword

nonn

Author

Amarnath Murthy, Nov 01 2003

Extensions

More terms from David Wasserman, Sep 09 2005

Status

approved