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A298313 The first of three consecutive primes the sum of which is equal to the sum of three consecutive octagonal numbers. 2
12541, 75521, 159617, 182519, 271181, 373091, 603901, 609289, 851197, 983819, 1246757, 2079997, 3299081, 3687421, 4484737, 4692497, 5636171, 7514477, 8273437, 9299831, 10408577, 10430921, 10746557, 10769281, 12739037, 13012487, 14213621, 15440531, 15713959 (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
12541 is in the sequence because 12541+12547+12553 (consecutive primes) = 37641 = 12160+12545+12936 (consecutive octagonal numbers).
MATHEMATICA
Module[{nn=5000, oct3}, oct3=Total/@Partition[PolygonalNumber[8, Range[nn]], 3, 1]; Select[ Partition[Prime[Range[PrimePi[Ceiling[Max[oct3]/3]]]], 3, 1], MemberQ[ oct3, Total[ #]]&]][[All, 1]] (* Harvey P. Dale, Dec 03 2022 *)
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, p))); Vec(L)
(Python)
from __future__ import division
from sympy import prevprime, nextprime
A298313_list, n, m = [], 1, 30
while len(A298313_list) < 10000:
k = prevprime(m//3)
k2 = prevprime(k)
k3 = nextprime(k)
if k2 + k + k3 == m:
A298313_list.append(k2)
elif k + k3 + nextprime(k3) == m:
A298313_list.append(k)
n += 1
m += 18*n + 3 # Chai Wah Wu, Jan 22 2018
CROSSREFS
Sequence in context: A231956 A252164 A045217 * A225151 A237907 A251296
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 17 2018
STATUS
approved

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Last modified September 21 02:47 EDT 2023. Contains 365486 sequences. (Running on oeis4.)