OFFSET
1,1
COMMENTS
Numbers p that are the first of three consecutive primes p,q,r such that p*q*r-(p+q+r) is the sum of two consecutive primes and p*q*r+(p+q+r) is the sum of two consecutive primes.
LINKS
Robert Israel, Table of n, a(n) for n = 1..1000
EXAMPLE
a(3) = 3967 is a term because 3967, 3989, 4001 are consecutive primes with
3967*3989*4001-(3967+3989+4001) = 63313264406 = 31656632197+31656632209,
3967*3989*4001+(3967+3989+4001) = 63313288320 = 31656644153+31656644167,
31656632197 and 31656632209 are consecutive primes
and 31656644153 and 31656644167 are consecutive primes.
MAPLE
q:= 2: r:= 3:
R:= NULL: count:= 0:
while count < 40 do
p:= q; q:= r; r:= nextprime(r);
s:= p+q+r;
v:= p*q*r+s;
t:= prevprime(v/2);
if nextprime(t)+t <> v then next fi;
v:= v-2*s;
t:= prevprime(v/2);
if nextprime(t)+t = v then
count:= count+1;
R:= R, p;
fi
od:
R;
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 26 2021
STATUS
approved