OFFSET
1,1
COMMENTS
The positive integer solutions of 24*p = x^2 - y^2 are (x = p+6, y = p-6), (x = 2*p+3, y = 2*p - 3), (x = 3*p+2, y = 3*p-2) and (x = 6*p+1, y=6*p-1). Since at least one of these is always divisible by 7, it is impossible for 24*p to be the difference of two squares of primes in 4 different ways.
Primes p such that three of the pairs (p +- 6), (2*p +- 3), (3*p +- 2), (6*p +- 1) are pairs of primes.
Except for 5, all terms == 3 or 7 (mod 10).
LINKS
Robert Israel, Table of n, a(n) for n = 1..1000
EXAMPLE
a(3) = 13 is a term because 13 is prime, 13 +- 6 = 19 and 7 are primes, 2*13 +- 3 = 29 and 23 are primes, and 3*13 +- 2 = 37 and 41 are primes.
MAPLE
filter:= proc(p) local t;
if not isprime(p) then return false fi;
t:= 0;
if isprime(p+6) and isprime(p-6) then t:= t+1 fi;
if isprime(2*p+3) and isprime(2*p-3) then t:= t+1 fi;
if isprime(3*p+2) and isprime(3*p-2) then t:= t+1 fi;
if isprime(6*p+1) and isprime(6*p-1) then t:= t+1 fi;
t = 3
end proc:
select(filter, [seq(i, i=3..10^7, 2)]);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Nov 08 2022
STATUS
approved