cp's OEIS Frontend

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

%I A195336 #21 Aug 06 2021 04:38:50
%S A195336 8,6,2,150,96,324,6,1518,174,168,21384,18,20754,2988,2424,8196,3786,
%T A195336 14952,34056,48,1620,8256,31344,1176,123360,147456,28650,132,90,12834,
%U A195336 81126,11790,2340,9702,11496,33000,10716,66954,6816,234,109956,3012,6744,117654,19950,26550,8226,40584,23640,30660
%N A195336 Smallest number k such that k^n is the sum of numbers in a twin prime pair.
%C A195336 Schinzel's hypothesis H implies that a(n) exists for every n. [_Charles R Greathouse IV_, Sep 18 2011]
%F A195336 a(n) is the least k such that (1/2)*k^n - 1 and (1/2)*k^n + 1 are prime.
%p A195336 isA054735 := proc(n)
%p A195336         if type(n,'odd') then
%p A195336                 false;
%p A195336         else
%p A195336                 isprime(n/2-1) and isprime(n/2+1) ;
%p A195336         end if;
%p A195336 end proc:
%p A195336 A195336 := proc(n)
%p A195336         for k from 1 do
%p A195336                 if isA054735(k^n) then
%p A195336                         return k;
%p A195336                 end if;
%p A195336         end do:
%p A195336 end proc:
%p A195336 for n from 1  do print(A195336(n)) ; end do: # _R. J. Mathar_, Sep 20 2011
%o A195336 (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
%o A195336 (Python)
%o A195336 from sympy import isprime
%o A195336 def cond(k, n): m = (k**n)//2; return isprime(m-1) and isprime(m+1)
%o A195336 def a(n):
%o A195336     k = 2
%o A195336     while not cond(k, n): k += 2
%o A195336     return k
%o A195336 print([a(n) for n in range(1, 25)]) # _Michael S. Branicky_, Aug 06 2021
%Y A195336 Cf. A054735.
%K A195336 nonn
%O A195336 1,1
%A A195336 _Kausthub Gudipati_, Sep 16 2011
%E A195336 a(11)-a(50) from _Charles R Greathouse IV_, Sep 18 2011