A298301 The first of three consecutive heptagonal numbers the sum of which is equal to the sum of three consecutive primes.

7, 874, 7209, 15484, 16687, 23863, 68641, 98704, 122877, 239785, 373842, 455182, 498852, 523723, 601966, 652036, 769230, 777573, 1003939, 1019844, 1121245, 1189215, 1203049, 1420159, 1484946, 1594804, 1606807, 1687977, 1804975, 2292973, 2533612, 3012363

Offset: 1

Author

Colin Barker, Jan 16 2018

Keywords

• nonn

Examples

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

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, A298302.

Programs

PARI

L=List(); forprime(p=2, 2000000, 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, (5*u^2-3*u)/2))); Vec(L)