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%I #12 Feb 11 2018 19:38:21
%S 2,7,31,61,73,271,373,521,619,983,2341,2843,3469,3559,4943,6211,7741,
%T 9173,12073,14869,24083,33923,40177,41611,43651,46349,47269,51031,
%U 53623,60719,64613,88397,91801,93089,114941,124739,126751,127249,134923,141769,145517
%N The first of three consecutive primes the sum of which is equal to the sum of three consecutive triangular numbers.
%H Chai Wah Wu, <a href="/A298169/b298169.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..300 from Colin Barker)
%e 31 is in the sequence because 7+11+13 (consecutive primes) = 31 = 6+10+15 (consecutive triangular numbers).
%o (PARI) L=List(); forprime(p=2, 400000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(24*t-15, &sq) && (sq-9)%6==0, listput(L, p))); Vec(L)
%Y Cf. A000040, A000217, A298168.
%K nonn
%O 1,1
%A _Colin Barker_, Jan 14 2018
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