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A298251 The first of three consecutive primes the sum of which is equal to the sum of three consecutive pentagonal numbers. 8
199, 35951, 46351, 69221, 88427, 230291, 490481, 707573, 829883, 1088419, 1129693, 1258109, 1736101, 1918157, 1976243, 2456939, 2741159, 2753351, 2822881, 3249419, 4603351, 5121713, 5528623, 6186407, 6664429, 6945559, 6964949, 7094839, 7120963, 7147121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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

MAPLE

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

Res:= NULL:

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

M3:= map(t->9/2*t^2+15/2*t+6, [seq(seq(4*i+j, j=2..3), i=0..mmax/4)]):

for m in M3 do

  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, p1

  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, p))); Vec(L)

CROSSREFS

Cf. A000040, A000326, A054643, A298073, A298168, A298169, A298222, A298223, A298250.

Sequence in context: A269549 A324436 A209181 * A097732 A305413 A181007

Adjacent sequences:  A298248 A298249 A298250 * A298252 A298253 A298254

KEYWORD

nonn

AUTHOR

Colin Barker, Jan 15 2018

STATUS

approved

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Last modified July 4 09:40 EDT 2020. Contains 335446 sequences. (Running on oeis4.)