login
A361930
a(n) is the greatest prime p such that p + q^2 + r^3 = prime(n)^4 for some primes q and r.
1
29, 613, 2389, 14629, 28549, 83227, 130171, 279707, 707131, 923509, 1873867, 2825749, 3418627, 4879669, 7890347, 12116969, 13845473, 20150467, 25411387, 28398229, 38949947, 47458027, 62740901, 88529269, 104060267, 112550869, 131079589, 141157867, 163046969, 260144491, 294499771, 352275349
OFFSET
2,1
COMMENTS
Conjecture: a(n) exists for all n > 2.
LINKS
EXAMPLE
a(2) = 29 because 29 + 5^2 + 3^3 = 81 = prime(2)^4, with 29, 5 and 3 prime.
a(3) = 613 because 613 + 2^2 + 2^3 = 625 = prime(3)^4. with 613, 2 and 2 prime.
MAPLE
Qs:= select(isprime, [$2..floor(sqrt(100000))]):
Rs:= select(isprime, [$2..floor(100000^(1/3))]):
QRs:= sort(select(t -> t[1]^2 + t[2]^3 < 100000, [seq(seq([q, r], q=Qs), r=Rs)]),
(a, b) -> a[1]^2 + a[2]^3 < b[1]^2 + b[2]^3):
f:= proc(t) local t4, qr, p;
t4:= t^4;
for qr in QRs do
p:= t4 - qr[1]^2 - qr[2]^3;
if isprime(p) then return p fi
od;
FAIL
end proc:
seq(f(ithprime(i)), i=2..50);
CROSSREFS
Cf. A030514 (prime(n)^4).
Sequence in context: A287050 A142521 A032630 * A014929 A006136 A199038
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Mar 30 2023
STATUS
approved