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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 28 13:14 EDT 2020. Contains 338055 sequences. (Running on oeis4.)