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%I #13 Feb 12 2018 09:54:25
%S 7,874,7209,15484,16687,23863,68641,98704,122877,239785,373842,455182,
%T 498852,523723,601966,652036,769230,777573,1003939,1019844,1121245,
%U 1189215,1203049,1420159,1484946,1594804,1606807,1687977,1804975,2292973,2533612,3012363
%N The first of three consecutive heptagonal numbers the sum of which is equal to the sum of three consecutive primes.
%H Chai Wah Wu, <a href="/A298301/b298301.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..100 from Colin Barker)
%e 7 is in the sequence because 7+18+34 (consecutive hexagonal numbers) = 59 = 17+19+23 (consecutive primes).
%o (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)
%Y Cf. A000040, A000566, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272, A298273, A298302.
%K nonn
%O 1,1
%A _Colin Barker_, Jan 16 2018
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