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

1,1

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

Cf. A000040, A000567, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272, A298273, A298301, A298302, A298312.

Sequence in context: A231956 A252164 A045217 * A225151 A237907 A251296

Adjacent sequences: A298310 A298311 A298312 * A298314 A298315 A298316

Keyword

nonn

Author

Colin Barker, Jan 17 2018

Status

approved