A308442 Primes of the form (p^k+1)/2 where p is prime and k > 1.

5, 13, 41, 61, 181, 313, 421, 1201, 1741, 1861, 2521, 3121, 5101, 7321, 8581, 9661, 14281, 16381, 19801, 36721, 41761, 60901, 71821, 83641, 100801, 106261, 135721, 139921, 161881, 163021, 199081, 205441, 218461, 273061, 282001, 337021, 353641, 388081, 431521, 491041, 531481, 539761, 552301, 571381

Offset

1,1

Comments

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

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

N:= 10^6: # to get terms <= N
p:= 2:
Res:= NULL:
do
  p:= nextprime(p);
  if p^2 >= 2*N then break fi;
  pk:= p;
  do
    pk:= pk^2;
    if pk >= 2*N then break fi;
    v:= (pk+1)/2;
    if isprime(v) then Res:= Res, v;
    fi;
  od
od:
sort([Res]); # Robert Israel, May 27 2019

Crossrefs

Cf. A076481.

Contains A067756.

Sequence in context: A103729 A234739 A027862 * A322155 A100210 A359730

Adjacent sequences: A308439 A308440 A308441 * A308443 A308444 A308445

Keyword

nonn

Author

J. M. Bergot and Robert Israel, May 27 2019

Status

approved