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

1,1

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