A298302 - OEIS

%I #12 Feb 12 2018 09:54:17

%S 17,967,7477,15877,17093,24337,69467,99689,123983,241333,375773,

%T 457307,501077,525983,604411,654587,772001,780347,1007099,1023037,

%U 1124593,1192651,1206497,1423921,1488797,1598791,1610809,1692071,1809221,2297759,2538623,3017849

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

%H Chai Wah Wu, <a href="/A298302/b298302.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..100 from Colin Barker)

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

%o (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)

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

%K nonn

%O 1,1

%A _Colin Barker_, Jan 16 2018