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

Author

Colin Barker, Jan 17 2018

Keywords

• nonn

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

Cf. A000040, A000567, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272, A298273, A298301, A298302, A298313.

Programs

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
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