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A298273
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The first of three consecutive primes the sum of which is equal to the sum of three consecutive hexagonal numbers.
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6
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13, 6427, 7873, 9439, 17203, 20287, 22783, 30133, 77417, 90523, 93949, 115903, 117841, 119797, 324403, 367649, 399163, 424573, 439441, 473839, 501493, 576193, 597859, 628861, 693223, 746023, 987697, 1044733, 1151399, 1212889, 1263247, 1360417, 1454351
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OFFSET
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1,1
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LINKS
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EXAMPLE
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13 is in the sequence because 13+17+19 (consecutive primes) = 49 = 6+15+28 (consecutive hexagonal numbers).
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MAPLE
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N:= 100: # to get a(1)..a(100)
count:= 0:
mmax:= floor((sqrt(24*N-87)-9)/12):
for i from 1 while count < N do
mi:= 2*i;
m:= 6*mi^2+9*mi+7;
r:= ceil((m-8)/3);
p1:= prevprime(r+1);
p2:= nextprime(p1);
p3:= nextprime(p2);
while p1+p2+p3 > m do
p3:= p2; p2:= p1; p1:= prevprime(p1);
od:
if p1+p2+p3 = m then
count:= count+1;
A[count]:= p1;
fi
od:
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PROG
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(PARI) L=List(); forprime(p=2, 2000000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(24*t-87, &sq) && (sq-9)%12==0, u=(sq-9)\12; listput(L, p))); Vec(L)
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CROSSREFS
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Cf. A000040, A000384, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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