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A298272
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The first of three consecutive hexagonal numbers the sum of which is equal to the sum of three consecutive primes.
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6
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6, 6216, 7626, 9180, 16836, 19900, 22366, 29646, 76636, 89676, 93096, 114960, 116886, 118828, 322806, 365940, 397386, 422740, 437580, 471906, 499500, 574056, 595686, 626640, 690900, 743590, 984906, 1041846, 1148370, 1209790, 1260078, 1357128, 1450956
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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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6 is in the sequence because 6+15+28 (consecutive hexagonal numbers) = 49 = 13+17+19 (consecutive primes).
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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]:= mi*(2*mi-1);
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, u*(2*u-1)))); Vec(L)
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CROSSREFS
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Cf. A000040, A000384, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298273.
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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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