A298466 The first of two consecutive primes the sum of which is equal to the sum of two consecutive heptagonal numbers.

3, 23, 433, 16481, 24593, 167953, 173183, 183871, 192097, 223781, 414521, 447743, 477857, 508951, 513473, 792983, 927803, 996019, 1034251, 1250309, 1285937, 2224063, 2281003, 2456191, 2607109, 2741561, 2773073, 3210353, 3336209, 4206817, 4403647, 4632161

Offset: 1

Author

Colin Barker, Jan 19 2018

Keywords

• nonn

Examples

			23 is in the sequence because 23+29 (consecutive primes) = 52 = 18+34 (consecutive heptagonal numbers).
		

Links

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

Crossrefs

Cf. A000040, A000566, A061275, A298462, A298463, A298464, A298465.

Programs

Mathematica

Module[{hep=Total/@Partition[PolygonalNumber[7,Range[1500]],2,1]},Select[ Partition[Prime[Range[PrimePi[Max[hep]/2]]],2,1],MemberQ[hep,Total[#]]&]][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 04 2019 *)

PARI

L=List(); forprime(p=2, 6000000, q=nextprime(p+1); t=p+q; if(issquare(20*t-16, &sq) && (sq-2)%10==0, u=(sq-2)\10; listput(L, p))); Vec(L)

Python

from sympy import prevprime, nextprime
A298466_list, n, m = [], 1 ,8
while len(A298466_list) < 10000:
    k = prevprime(m//2)
    if k + nextprime(k) == m:
        A298466_list.append(k)
    n += 1
    m += 10*n-3 # Chai Wah Wu, Jan 19 2018