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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
Sequence in context: A018235 A250837 A234079 * A167729 A115674 A013819
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 17 2018
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)