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A298273 The first of three consecutive primes the sum of which is equal to the sum of three consecutive hexagonal numbers. 6
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 (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

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: A103857 A263160 A032463 * A203585 A191937 A210157

Adjacent sequences:  A298270 A298271 A298272 * A298274 A298275 A298276

KEYWORD

nonn

AUTHOR

Colin Barker, Jan 16 2018

STATUS

approved

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)