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

1,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A159647 A111454 A116421 * A260655 A318598 A215229

Adjacent sequences: A298462 A298463 A298464 * A298466 A298467 A298468

Keyword

nonn

Author

Colin Barker, Jan 19 2018

Status

approved