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URL: https://oeis.org/A298250

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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
OFFSET
1,1
LINKS
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
MATHEMATICA
Module[{prs3=Total/@Partition[Prime[Range[10^6]], 3, 1]}, Select[ Partition[ PolygonalNumber[ 5, Range[ 5000]], 3, 1], MemberQ[ prs3, Total[#]]&]][[All, 1]] (* Harvey P. Dale, Dec 25 2022 *)
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)
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 15 2018
STATUS
approved