A298312 The first of three consecutive octagonal numbers the sum of which is equal to the sum of three consecutive primes.
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
Offset: 1
Keywords
Examples
12160 is in the sequence because 12160+12545+12936 (consecutive octagonal numbers) = 37641 = 12541+12547+12553 (consecutive primes).
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..70 from Colin Barker)
Crossrefs
Programs
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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)
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Python
from _future_ import division from sympy import prevprime, nextprime A298312_list, n, m = [], 1, 30 while len(A298312_list) < 10000: k = prevprime(m//3) k2 = nextprime(k) if prevprime(k) + k + k2 == m or k + k2 + nextprime(k2) == m: A298312_list.append(n*(3*n-2)) n += 1 m += 18*n + 3 # Chai Wah Wu, Jan 22 2018