A195336 Smallest number k such that k^n is the sum of numbers in a twin prime pair.

8, 6, 2, 150, 96, 324, 6, 1518, 174, 168, 21384, 18, 20754, 2988, 2424, 8196, 3786, 14952, 34056, 48, 1620, 8256, 31344, 1176, 123360, 147456, 28650, 132, 90, 12834, 81126, 11790, 2340, 9702, 11496, 33000, 10716, 66954, 6816, 234, 109956, 3012, 6744, 117654, 19950, 26550, 8226, 40584, 23640, 30660

Offset

1,1

Comments

Schinzel's hypothesis H implies that a(n) exists for every n. [Charles R Greathouse IV, Sep 18 2011]

Links

Table of n, a(n) for n=1..50.

Formula

a(n) is the least k such that (1/2)*k^n - 1 and (1/2)*k^n + 1 are prime.

Maple

isA054735 := proc(n)
        if type(n, 'odd') then
                false;
        else
                isprime(n/2-1) and isprime(n/2+1) ;
        end if;
end proc:
A195336 := proc(n)
        for k from 1 do
                if isA054735(k^n) then
                        return k;
                end if;
        end do:
end proc:
for n from 1  do print(A195336(n)) ; end do: # R. J. Mathar, Sep 20 2011

Prog

(PARI) a(n)=my(k=2); while(!ispseudoprime(k^n/2-1)||!ispseudoprime(k^n/2+1), k+=2); k \\ Charles R Greathouse IV, Sep 18 2011
(Python)
from sympy import isprime
def cond(k, n): m = (k**n)//2; return isprime(m-1) and isprime(m+1)
def a(n):
    k = 2
    while not cond(k, n): k += 2
    return k
print([a(n) for n in range(1, 25)]) # Michael S. Branicky, Aug 06 2021

Crossrefs

Cf. A054735.

Sequence in context: A316588 A323810 A342946 * A196773 A197824 A085666

Adjacent sequences: A195333 A195334 A195335 * A195337 A195338 A195339

Keyword

nonn

Author

Kausthub Gudipati, Sep 16 2011

Extensions

a(11)-a(50) from Charles R Greathouse IV, Sep 18 2011

Status

approved