cp's OEIS Frontend

A298273 The first of three consecutive primes the sum of which is equal to the sum of three consecutive hexagonal numbers.

%I A298273 #11 Jan 17 2018 11:45:54
%S A298273 13,6427,7873,9439,17203,20287,22783,30133,77417,90523,93949,115903,
%T A298273 117841,119797,324403,367649,399163,424573,439441,473839,501493,
%U A298273 576193,597859,628861,693223,746023,987697,1044733,1151399,1212889,1263247,1360417,1454351
%N A298273 The first of three consecutive primes the sum of which is equal to the sum of three consecutive hexagonal numbers.
%H A298273 Robert Israel, <a href="/A298273/b298273.txt">Table of n, a(n) for n = 1..10000</a> (first 100 terms from Colin Barker)
%e A298273 13 is in the sequence because 13+17+19 (consecutive primes) = 49 = 6+15+28 (consecutive hexagonal numbers).
%p A298273 N:= 100: # to get a(1)..a(100)
%p A298273 count:= 0:
%p A298273 mmax:= floor((sqrt(24*N-87)-9)/12):
%p A298273 for i from 1 while count < N do
%p A298273   mi:= 2*i;
%p A298273   m:= 6*mi^2+9*mi+7;
%p A298273   r:= ceil((m-8)/3);
%p A298273   p1:= prevprime(r+1);
%p A298273   p2:= nextprime(p1);
%p A298273   p3:= nextprime(p2);
%p A298273   while p1+p2+p3 > m do
%p A298273     p3:= p2; p2:= p1; p1:= prevprime(p1);
%p A298273   od:
%p A298273   if p1+p2+p3 = m then
%p A298273     count:= count+1;
%p A298273   A[count]:= p1;
%p A298273   fi
%p A298273 od:
%p A298273 seq(A[i],i=1..count); # _Robert Israel_, Jan 16 2018
%o A298273 (PARI) L=List(); forprime(p=2, 2000000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(24*t-87, &sq) && (sq-9)%12==0, u=(sq-9)\12; listput(L, p))); Vec(L)
%Y A298273 Cf. A000040, A000384, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272.
%K A298273 nonn
%O A298273 1,1
%A A298273 _Colin Barker_, Jan 16 2018