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

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..70 from Colin Barker)

Example

12160 is in the sequence because 12160+12545+12936 (consecutive octagonal numbers) = 37641 = 12541+12547+12553 (consecutive primes).

Prog

(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

Crossrefs

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

Sequence in context: A018235 A250837 A234079 * A167729 A115674 A013819

Adjacent sequences: A298309 A298310 A298311 * A298313 A298314 A298315

Keyword

nonn

Author

Colin Barker, Jan 17 2018

Status

approved