A298272 The first of three consecutive hexagonal numbers the sum of which is equal to the sum of three consecutive primes.

6, 6216, 7626, 9180, 16836, 19900, 22366, 29646, 76636, 89676, 93096, 114960, 116886, 118828, 322806, 365940, 397386, 422740, 437580, 471906, 499500, 574056, 595686, 626640, 690900, 743590, 984906, 1041846, 1148370, 1209790, 1260078, 1357128, 1450956

Offset

1,1

Links

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

Example

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

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]:= mi*(2*mi-1);
  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, u*(2*u-1)))); Vec(L)

Crossrefs

Cf. A000040, A000384, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298273.

Sequence in context: A111152 A202969 A003191 * A000438 A061109 A321983

Adjacent sequences: A298269 A298270 A298271 * A298273 A298274 A298275

Keyword

nonn

Author

Colin Barker, Jan 16 2018

Status

approved