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A089306 Smallest prime of the form n + (n+1)+ (n+2)+...+(n+k), or 0 if no such prime exists. 9
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 (list; graph; refs; listen; history; text; internal format)
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.

Positions of zeros are listed in A077654. [Paolo P. Lava, Jun 06 2013]

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

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Last modified September 28 21:38 EDT 2020. Contains 337397 sequences. (Running on oeis4.)