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A203619
Numbers that are a sum of m=3 successive primes and also a product of m=3 (other) successive primes.
7
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
KEYWORD
nonn
AUTHOR
Zak Seidov, Feb 09 2012
STATUS
approved