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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.

%I A298464 #12 Jan 22 2018 03:20:38
%S A298464 79,3643,10909,37123,56053,70849,78889,125551,178877,209063,258743,
%T A298464 330409,350411,395261,439559,469279,479387,499969,620813,663997,
%U A298464 754723,828811,878597,901709,1026709,1087147,1170397,1202429,1213189,1234873,1340477,1510013
%N A298464 The first of two consecutive primes the sum of which is equal to the sum of two consecutive pentagonal numbers.
%H A298464 Chai Wah Wu, <a href="/A298464/b298464.txt">Table of n, a(n) for n = 1..10000</a>
%e A298464 79 is in the sequence because 79+83 (consecutive primes) = 162 = 70+92 (consecutive pentagonal numbers).
%t A298464 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 *)
%o A298464 (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)
%o A298464 (Python)
%o A298464 from __future__ import division
%o A298464 from sympy import prevprime, nextprime
%o A298464 A298464_list, n, m = [], 1 ,6
%o A298464 while len(A298464_list) < 10000:
%o A298464     k = prevprime(m//2)
%o A298464     if k + nextprime(k) == m:
%o A298464         A298464_list.append(k)
%o A298464     n += 1
%o A298464     m += 6*n-1 # _Chai Wah Wu_, Jan 20 2018
%Y A298464 Cf. A000040, A000326, A061275, A298462, A298463, A298465, A298466.
%K A298464 nonn
%O A298464 1,1
%A A298464 _Colin Barker_, Jan 19 2018