A203619 Numbers that are a sum of m=3 successive primes and also a product of m=3 (other) successive primes.

33263, 7566179, 10681031, 29884301, 51881689, 94593973, 182918137, 187466723, 319512181, 682238471, 799964687, 3926804047, 4047409651, 4881262679, 11857438631, 13418999327, 19184166361, 20428396159, 20743879777, 32573603551, 34148299187, 56372241473, 72215998451

Offset

1,1

Comments

Indices of initial addends (summands) are 1343, 184557, 254101, 662222, 1108908, 1946623, 3616497, 3700883, 6114024, 12508273, 14539139, 65654476, 67568267, 80729196.

Initial addends (summands) are 11083, 2522057, 3560329, 9961421, 17293891, 31531301, 60972697, 62488883, 106504039, 227412803, 266654879, 1308934661, 1349136511, 1627087549.

Indices of initial factors are 10, 44, 47, 63, 73, 87, 103, 104, 123, 151, 157, 248, 250, 264.

Initial factors are 29, 193, 211, 307, 367, 449, 563, 569, 677, 877, 919, 1571, 1583, 1693.

Links

Zak Seidov and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

33263 = 11083+11087+11093 = 29*31*37,
7566179 = 2522057+2522059+2522063 = 193*197*199,
10681031 = 3560329+3560339+3560363 = 211*223*227,
4881262679 = 1627087549+1627087559+1627087571 = 1693*1697*1699.

Prog

(PARI) list(lim)={
    my(v=List(), p, q, p1, q1, r1, t);
    t=nextprime(lim^(1/3));
    while(t*precprime(t-1)*precprime(precprime(t-1)-1)<lim, t=nextprime(t+1));
    p=2; q=3;
    forprime(r=5, precprime(t-1),
        t=p*q*r;
        q1=nextprime(t\3);
        p1=precprime(q1-1);
        r1=nextprime(q1+1);
        while(p1+q1+r1<t, p1=q1; q1=r1; r1=nextprime(r1+1));
        while(p1+q1+r1>t, r1=q1; q1=p1; p1=precprime(p1-1));
        if(p1+q1+r1==t, listput(v, t));
        p=q; q=r
    );
    Vec(v)
}; \\ Charles R Greathouse IV, Feb 13 2012

Crossrefs

Intersection of A034961 and A046301.

Cf. A034961 (sums of three consecutive primes), A046301 (product of 3 successive primes).

Sequence in context: A332200 A031660 A252291 * A170798 A043628 A205410

Adjacent sequences: A203616 A203617 A203618 * A203620 A203621 A203622

Keyword

nonn

Author

Zak Seidov, Feb 09 2012

Status

approved