A298464 The first of two consecutive primes the sum of which is equal to the sum of two consecutive pentagonal numbers.

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

Offset: 1

Author

Colin Barker, Jan 19 2018

Keywords

• nonn

Examples

			79 is in the sequence because 79+83 (consecutive primes) = 162 = 70+92 (consecutive pentagonal numbers).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000326, A061275, A298462, A298463, A298465, A298466.

Programs

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 *)

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