OFFSET
1,1
COMMENTS
Dickson's conjecture implies that there are infinitely many terms with, for example, the first three consecutive primes p, p+2, p+6 and the second three 13*p+36, 13*p+38 and 13*p+42.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 31 is a term because 31, 37, 41 are consecutive primes and 41^2-31^2+31 = 751, 41^2-31^2+37 = 757, 41^2-31^2+41 = 761 are consecutive primes.
MAPLE
R:= NULL: count:= 0:
q:= 2: r:= 3:
while count < 50 do
p:= q; q:= r; r:= nextprime(r);
d:= r^2 - p^2;
if isprime(p+d) and nextprime(p+d)=q+d and nextprime(q+d)=r+d then
count:= count+1; R:= R, p
fi
od:
R;
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Mar 10 2022
STATUS
approved