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A298312 The first of three consecutive octagonal numbers the sum of which is equal to the sum of three consecutive primes.

%I A298312 #13 Jan 22 2018 15:32:51
%S A298312 12160,74576,158240,181056,269400,371008,601216,606600,848008,980408,
%T A298312 1242920,2075008,3292816,3680776,4477408,4685000,5627960,7505008,
%U A298312 8263480,9289280,10397408,10419760,10735208,10757920,12726680,13000008,14200576,15426936,15700256
%N A298312 The first of three consecutive octagonal numbers the sum of which is equal to the sum of three consecutive primes.
%H A298312 Chai Wah Wu, <a href="/A298312/b298312.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..70 from Colin Barker)
%e A298312 12160 is in the sequence because 12160+12545+12936 (consecutive octagonal numbers) = 37641 = 12541+12547+12553 (consecutive primes).
%o A298312 (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)
%o A298312 (Python)
%o A298312 from __future__ import division
%o A298312 from sympy import prevprime, nextprime
%o A298312 A298312_list, n, m = [], 1, 30
%o A298312 while len(A298312_list) < 10000:
%o A298312     k = prevprime(m//3)
%o A298312     k2 = nextprime(k)
%o A298312     if prevprime(k) + k + k2 == m or k + k2 + nextprime(k2) == m:
%o A298312         A298312_list.append(n*(3*n-2))
%o A298312     n += 1
%o A298312     m += 18*n + 3 # _Chai Wah Wu_, Jan 22 2018
%Y A298312 Cf. A000040, A000567, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272, A298273, A298301, A298302, A298313.
%K A298312 nonn
%O A298312 1,1
%A A298312 _Colin Barker_, Jan 17 2018