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A288574 Total number of distinct primes in all representations of 2*n+1 as a sum of 3 odd primes. 3
0, 0, 0, 0, 1, 2, 4, 4, 6, 7, 9, 10, 12, 15, 17, 16, 19, 19, 23, 25, 26, 26, 28, 33, 32, 35, 43, 39, 41, 45, 45, 48, 54, 55, 52, 60, 59, 56, 75, 67, 67, 81, 74, 76, 92, 83, 85, 100, 96, 81, 106, 103, 91, 121, 108, 98, 131, 120, 116, 143, 133, 129, 151, 144, 124, 163 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

That is, a representation 2n+1 = p+p+p counts as 1, as p+p+q counts as 2, and p+q+r counts as 3. If each representation is counted once, we simply get A007963.

LINKS

Indranil Ghosh (first 200 terms), Hugo Pfoertner, Table of n, a(n) for n = 0..10000

MAPLE

A288574 := proc(n)

    local a, i, j, k, p, q, r, pqr ;

    a := 0 ;

    for i from 2 do

        p := ithprime(i) ;

        for j from i do

            q := ithprime(j) ;

            for k from j do

                r := ithprime(k) ;

                if p+q+r = 2*n+1 then

                    pqr := {p, q, r} ;

                    a := a+nops(pqr) ;

                elif p+q+r > 2*n+1 then

                    break;

                end if;

            end do:

            if p+2*q > 2*n+1 then

                break;

            end if;

        end do:

        if 3*p > 2*n+1 then

            break;

        end if;

    end do:

    return a;

end proc:

seq(A288574(n), n=0..80) ; # R. J. Mathar, Jun 29 2017

PROG

(PARI) a(n)={my(p, q, r, cnt); n=2*n+1;

forprime(p=3, n\3, forprime(q=p, (n-p)\2,

if(isprime(r=n-p-q), cnt+=if(p===q&&p==r, 1, if(p==q||q==r, 2, 3))))); cnt}

\\ Franklin T. Adams-Watters, Jun 28 2017

(Python)

from sympy import primerange, isprime, floor

def a(n):

    n=2*n + 1

    c=0

    for p in primerange(3, floor(n/3) + 1):

        for q in primerange(p, floor((n - p)/2) + 1):

            r=n - p - q

            if isprime(r): c+=1 if p==q and p==r else 2 if p==q or q==r else 3

    return c

print [a(n) for n in range(0, 66)] # Indranil Ghosh, Jun 29 2017

CROSSREFS

A288573 appears to be an erroneous version of this sequence.

Cf. A007963, A054860, A087916.

Sequence in context: A026413 A038669 A288573 * A135692 A089003 A132118

Adjacent sequences:  A288571 A288572 A288573 * A288575 A288576 A288577

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters and R. J. Mathar, Jun 28 2017

STATUS

approved

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Last modified March 30 09:41 EDT 2020. Contains 333125 sequences. (Running on oeis4.)