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%I #7 Jan 15 2018 09:39:41
%S 1511,5923,6553,9791,11003,14153,14633,15121,22787,29231,36473,61991,
%T 62987,68111,89393,116273,137633,167267,212501,233279,292673,316957,
%U 426401,455603,579113,603719,717397,819017,938953,1018057,1022113,1292737,1399477,1510427
%N The first of three consecutive primes the sum of which is equal to the sum of three consecutive squares.
%H Colin Barker, <a href="/A298223/b298223.txt">Table of n, a(n) for n = 1..100</a>
%e 1511 is in the sequence because 1511+1523+1531 (consecutive primes) = 4565 = 1444+1521+1600 (consecutive squares).
%o (PARI) L=List(); forprime(p=2, 400000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(12*t-24, &sq) && (sq-6)%6==0, u=(sq-6)\6; listput(L, p))); Vec(L)
%Y Cf. A000040, A000290, A054643, A298073, A298168, A298169, A298222.
%K nonn
%O 1,1
%A _Colin Barker_, Jan 15 2018
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