A308442 - OEIS

%I #10 May 29 2019 05:25:54

%S 5,13,41,61,181,313,421,1201,1741,1861,2521,3121,5101,7321,8581,9661,

%T 14281,16381,19801,36721,41761,60901,71821,83641,100801,106261,135721,

%U 139921,161881,163021,199081,205441,218461,273061,282001,337021,353641,388081,431521,491041,531481,539761,552301,571381

%N Primes of the form (p^k+1)/2 where p is prime and k > 1.

%C The only primes of the form (p^k-1)/2 are A076481, since (p^k-1)/2 is divisible by (p-1)/2.

%C k must be a power of 2, since if k has an odd divisor d>1, (p^k+1)/2 is divisible by (p^(k/d)+1)/2.

%H Robert Israel, <a href="/A308442/b308442.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 41 is in the sequence because 41 = (3^4 + 1)/2.

%p N:= 10^6: # to get terms <= N

%p p:= 2:

%p Res:= NULL:

%p do

%p   p:= nextprime(p);

%p   if p^2 >= 2*N then break fi;

%p   pk:= p;

%p   do

%p     pk:= pk^2;

%p     if pk >= 2*N then break fi;

%p     v:= (pk+1)/2;

%p     if isprime(v) then Res:= Res, v;

%p     fi;

%p   od

%p od:

%p sort([Res]); # _Robert Israel_, May 27 2019

%Y Cf. A076481.

%Y Contains A067756.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, May 27 2019