A301619 - OEIS

%I #16 Sep 08 2022 08:46:20

%S 257,449,641,1217,1409,1601,2753,3137,3329,4289,4481,4673,5441,6977,

%T 7937,8513,9281,9473,9857,10433,11393,11777,11969,12161,13121,13313,

%U 13697,14081,14657,15233,15809,16001,16193,17729,17921,19073,19457,19841,21377,21569

%N Primes congruent to 65 (mod 192).

%C In other words, primes of the form 192*k+65 for k > 0.

%H R. Scott and R. Styer, <a href="https://doi.org/10.1016/j.jnt.2003.11.008">On p^x - q^y = c and related three term exponential Diophantine equations with prime bases</a>, Journal of Number Theory, Vol. 105, No. 2 (2004), 212-234. See p. 218.

%t Select[Prime[Range[2500]], MemberQ[{65}, Mod[#, 192]] &] (* _Vincenzo Librandi_, Jan 04 2020 *)

%o (PARI) forprime(p=1, 5e4, if(Mod(p, 192)==65, print1(p, ", ")))

%o (Magma) [p: p in PrimesUpTo(25000) | p mod 192 in {65}]; // _Vincenzo Librandi_, Jan 04 2020

%Y Subsequence of A002144 (primes of form 4*k+65) and A007519 (primes of form 8*k+65).

%Y Cf. primes congruent to 65 (mod k): A142068 (k=66), A142137 (k=74), A142221 (k=82), A142271 (k=86), A142369 (k=94), A142427 (k=98), A142485 (k=102), A142542 (k=106), A142670 (k=114), A142733 (k=118), A142802 (k=122), A142890 (k=126), A105129 (k=128).

%K nonn,easy

%O 1,1

%A _Felix Fröhlich_, Mar 24 2018