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

%I A298465 #15 Oct 12 2023 13:38:32
%S A298465 1,18,403,16281,24354,167314,172528,183196,191407,223054,413512,
%T A298465 446688,476767,507826,512343,791578,926289,994456,1032658,1248562,
%U A298465 1284147,2221708,2278630,2453716,2604571,2738952,2770443,3207523,3333330,4203577,4400332,4628761
%N A298465 The first of two consecutive heptagonal numbers the sum of which is equal to the sum of two consecutive primes.
%H A298465 Chai Wah Wu, <a href="/A298465/b298465.txt">Table of n, a(n) for n = 1..10000</a>
%e A298465 18 is in the sequence because 18+34 (consecutive heptagonal numbers) = 52 = 23+29 (consecutive primes).
%t A298465 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 *)
%o A298465 (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)
%o A298465 (Python)
%o A298465 from sympy import prevprime, nextprime
%o A298465 A298465_list, n, m = [], 1 ,8
%o A298465 while len(A298465_list) < 10000:
%o A298465     k = prevprime(m//2)
%o A298465     if k + nextprime(k) == m:
%o A298465         A298465_list.append(n*(5*n-3)//2)
%o A298465     n += 1
%o A298465     m += 10*n-3 # _Chai Wah Wu_, Jan 19 2018
%Y A298465 Cf. A000040, A000566, A061275, A298462, A298463, A298464, A298466.
%K A298465 nonn
%O A298465 1,2
%A A298465 _Colin Barker_, Jan 19 2018