login
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
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)
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 16 2018
STATUS
approved