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 A298464 The first of two consecutive primes the sum of which is equal to the sum of two consecutive pentagonal numbers. 5
 79, 3643, 10909, 37123, 56053, 70849, 78889, 125551, 178877, 209063, 258743, 330409, 350411, 395261, 439559, 469279, 479387, 499969, 620813, 663997, 754723, 828811, 878597, 901709, 1026709, 1087147, 1170397, 1202429, 1213189, 1234873, 1340477, 1510013 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 EXAMPLE 79 is in the sequence because 79+83 (consecutive primes) = 162 = 70+92 (consecutive pentagonal numbers). MATHEMATICA Block[{s = Total /@ Partition[PolygonalNumber[5, Range[10^3]], 2, 1], t}, t = Partition[Prime@ Range@ PrimePi[2 Last[s]], 2, 1]; Select[t, MemberQ[s, Total@ #] &][[All, 1]]] (* Michael De Vlieger, Jan 21 2018 *) PROG (PARI) L=List(); forprime(p=2, 1600000, q=nextprime(p+1); t=p+q; if(issquare(12*t-8, &sq) && (sq-2)%6==0, u=(sq-2)\6; listput(L, p))); Vec(L) (Python) from __future__ import division from sympy import prevprime, nextprime A298464_list, n, m = [], 1 , 6 while len(A298464_list) < 10000: k = prevprime(m//2) if k + nextprime(k) == m: A298464_list.append(k) n += 1 m += 6*n-1 # Chai Wah Wu, Jan 20 2018 CROSSREFS Cf. A000040, A000326, A061275, A298462, A298463, A298465, A298466. Sequence in context: A205496 A017795 A017742 * A078114 A038531 A032910 Adjacent sequences: A298461 A298462 A298463 * A298465 A298466 A298467 KEYWORD nonn AUTHOR Colin Barker, Jan 19 2018 STATUS approved

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Last modified May 29 19:57 EDT 2024. Contains 372952 sequences. (Running on oeis4.)