OFFSET
1,3
COMMENTS
a(n) is the least term of A086119 such that a(n)/2^n is an odd prime, or -1 if there is no such term.
Since p^3 + q^3 = (p+q)*(p^2 - p*q + q^2), we must have p+q = 2^n, and p^2 - p*q + q^2 an odd prime.
Is a(n) > 0 for all n > 7?
EXAMPLE
a(3) = 152 because 3^3 + 5^3 = 152 = 2^3 * 19, 3 and 5 are primes and 19 is odd, and no smaller number works.
MAPLE
f:= proc(n) local p, q, t;
t:= 2^n; p:= nextprime(t/2);
while p > 2 do
p:= prevprime(p);
q:= t - p;
if isprime(q) and isprime(p^2 - p*q + q^2) then return p^3 + q^3 fi
od;
-1
end proc:
map(f, [$1..20]);
CROSSREFS
KEYWORD
sign
AUTHOR
Robert Israel, Jan 01 2023
STATUS
approved