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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 June 24 21:16 EDT 2019. Contains 324337 sequences. (Running on oeis4.)