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

13, 6427, 7873, 9439, 17203, 20287, 22783, 30133, 77417, 90523, 93949, 115903, 117841, 119797, 324403, 367649, 399163, 424573, 439441, 473839, 501493, 576193, 597859, 628861, 693223, 746023, 987697, 1044733, 1151399, 1212889, 1263247, 1360417, 1454351

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 100 terms from Colin Barker)

Example

13 is in the sequence because 13+17+19 (consecutive primes) = 49 = 6+15+28 (consecutive hexagonal numbers).

Maple

N:= 100: # to get a(1)..a(100)
count:= 0:
mmax:= floor((sqrt(24*N-87)-9)/12):
for i from 1 while count < N do
  mi:= 2*i;
  m:= 6*mi^2+9*mi+7;
  r:= ceil((m-8)/3);
  p1:= prevprime(r+1);
  p2:= nextprime(p1);
  p3:= nextprime(p2);
  while p1+p2+p3 > m do
    p3:= p2; p2:= p1; p1:= prevprime(p1);
  od:
  if p1+p2+p3 = m then
    count:= count+1;
  A[count]:= p1;
  fi
od:
seq(A[i], i=1..count); # Robert Israel, Jan 16 2018

Prog

(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)

Crossrefs

Cf. A000040, A000384, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298272.

Sequence in context: A263160 A373884 A032463 * A203585 A191937 A210157

Adjacent sequences: A298270 A298271 A298272 * A298274 A298275 A298276

Keyword

nonn

Author

Colin Barker, Jan 16 2018

Status

approved