A298302 The first of three consecutive primes the sum of which is equal to the sum of three consecutive heptagonal numbers.

17, 967, 7477, 15877, 17093, 24337, 69467, 99689, 123983, 241333, 375773, 457307, 501077, 525983, 604411, 654587, 772001, 780347, 1007099, 1023037, 1124593, 1192651, 1206497, 1423921, 1488797, 1598791, 1610809, 1692071, 1809221, 2297759, 2538623, 3017849

Offset: 1

Author

Colin Barker, Jan 16 2018

Keywords

• nonn

Examples

			17 is in the sequence because 17+19+23 (consecutive primes) = 59 = 7+18+34 (consecutive hexagonal numbers).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..100 from Colin Barker)

Crossrefs

Cf. A000040, A000566, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272, A298273, A298301.

Programs

PARI

L=List(); forprime(p=2, 4000000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(120*t-519, &sq) && (sq-21)%30==0, u=(sq-21)\30; listput(L, p))); Vec(L)