A298465 The first of two consecutive heptagonal numbers the sum of which is equal to the sum of two consecutive primes.

1, 18, 403, 16281, 24354, 167314, 172528, 183196, 191407, 223054, 413512, 446688, 476767, 507826, 512343, 791578, 926289, 994456, 1032658, 1248562, 1284147, 2221708, 2278630, 2453716, 2604571, 2738952, 2770443, 3207523, 3333330, 4203577, 4400332, 4628761

Offset: 1

Author

Colin Barker, Jan 19 2018

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A000040, A000566, A061275, A298462, A298463, A298464, A298466.

Programs

Mathematica

chcpQ[{a_,b_}]:=Module[{c=(a+b)/2},NextPrime[c]+ NextPrime[c,-1] ==a+b]; Select[ Partition[PolygonalNumber[7,Range[2000]],2,1],chcpQ][[;;,1]] (* Harvey P. Dale, Mar 14 2023 *)

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, (5*u^2-3*u)/2))); Vec(L)

Python

from sympy import prevprime, nextprime
A298465_list, n, m = [], 1 ,8
while len(A298465_list) < 10000:
    k = prevprime(m//2)
    if k + nextprime(k) == m:
        A298465_list.append(n*(5*n-3)//2)
    n += 1
    m += 10*n-3 # Chai Wah Wu, Jan 19 2018