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A308442
Primes of the form (p^k+1)/2 where p is prime and k > 1.
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, May 27 2019
STATUS
approved