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A298250 The first of three consecutive pentagonal numbers the sum of which is equal to the sum of three consecutive primes. 8
176, 35497, 45850, 68587, 87725, 229126, 488776, 705551, 827702, 1085876, 1127100, 1255380, 1732900, 1914785, 1972840, 2453122, 2737126, 2749297, 2818776, 3245026, 4598126, 5116190, 5522882, 6180335, 6658120, 6939126, 6958497, 7088327, 7114437, 7140595 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..2352

EXAMPLE

176 is in the sequence because 176+210+247 (consecutive pentagonal numbers) = 633 = 199+211+223 (consecutive primes).

MAPLE

N:= 10^8: # to get all terms where the sums <= N

Res:= NULL:

mmax:= floor((sqrt(8*N-23)-5)/6):

M:= [seq(seq(4*i+j, j=2..3), i=0..mmax/4)]:

M3:= map(m -> 9/2*m^2+15/2*m+6, M):

for i from 1 to nops(M) do

m:= M3[i];

  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

    Res:= Res, M[i]*(3*M[i]-1)/2;

  fi

od:

Res; # Robert Israel, Jan 16 2018

PROG

(PARI) L=List(); forprime(p=2, 8000000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(72*t-207, &sq) && (sq-15)%18==0, u=(sq-15)\18; listput(L, (3*u^2-u)/2))); Vec(L)

CROSSREFS

Cf. A000040, A000326, A054643, A298073, A298168, A298169, A298222, A298223, A298251.

Sequence in context: A229317 A035829 A284073 * A184293 A159426 A009722

Adjacent sequences:  A298247 A298248 A298249 * A298251 A298252 A298253

KEYWORD

nonn

AUTHOR

Colin Barker, Jan 15 2018

STATUS

approved

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Last modified July 9 11:58 EDT 2020. Contains 335543 sequences. (Running on oeis4.)