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A298272 The first of three consecutive hexagonal numbers the sum of which is equal to the sum of three consecutive primes. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 25 08:26 EDT 2020. Contains 334585 sequences. (Running on oeis4.)