A298169 The first of three consecutive primes the sum of which is equal to the sum of three consecutive triangular numbers.

2, 7, 31, 61, 73, 271, 373, 521, 619, 983, 2341, 2843, 3469, 3559, 4943, 6211, 7741, 9173, 12073, 14869, 24083, 33923, 40177, 41611, 43651, 46349, 47269, 51031, 53623, 60719, 64613, 88397, 91801, 93089, 114941, 124739, 126751, 127249, 134923, 141769, 145517

Offset: 1

Author

Colin Barker, Jan 14 2018

Keywords

• nonn

Examples

			31 is in the sequence because 7+11+13 (consecutive primes) = 31 = 6+10+15 (consecutive triangular numbers).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..300 from Colin Barker)

Crossrefs

Cf. A000040, A000217, A298168.

Programs

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)