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A298312
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The first of three consecutive octagonal numbers the sum of which is equal to the sum of three consecutive primes.
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2
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12160, 74576, 158240, 181056, 269400, 371008, 601216, 606600, 848008, 980408, 1242920, 2075008, 3292816, 3680776, 4477408, 4685000, 5627960, 7505008, 8263480, 9289280, 10397408, 10419760, 10735208, 10757920, 12726680, 13000008, 14200576, 15426936, 15700256
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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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12160 is in the sequence because 12160+12545+12936 (consecutive octagonal numbers) = 37641 = 12541+12547+12553 (consecutive primes).
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PROG
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(PARI) L=List(); forprime(p=2, 20000000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(36*t-180, &sq) && (sq-12)%18==0, u=(sq-12)\18; listput(L, 3*u^2-2*u))); Vec(L)
(Python)
from __future__ import division
from sympy import prevprime, nextprime
k = prevprime(m//3)
k2 = nextprime(k)
if prevprime(k) + k + k2 == m or k + k2 + nextprime(k2) == m:
n += 1
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CROSSREFS
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Cf. A000040, A000567, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272, A298273, A298301, A298302, A298313.
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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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