A298313 The first of three consecutive primes the sum of which is equal to the sum of three consecutive octagonal numbers.
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
Offset: 1
Keywords
Examples
12541 is in the sequence because 12541+12547+12553 (consecutive primes) = 37641 = 12160+12545+12936 (consecutive octagonal numbers).
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..70 from Colin Barker)
Crossrefs
Programs
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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 *) -
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)
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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