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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 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

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