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

Author

Kausthub Gudipati, Sep 16 2011

Keywords

• nonn

Comments

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

Crossrefs

Cf. A054735.

Programs

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

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

Formula

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

Extensions

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