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

Author

Zak Seidov, Feb 09 2012

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Intersection of A034961 and A046301.

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

Programs

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)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