cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A301619 Primes congruent to 65 (mod 192).

This page as a plain text file.
%I A301619 #16 Sep 08 2022 08:46:20
%S A301619 257,449,641,1217,1409,1601,2753,3137,3329,4289,4481,4673,5441,6977,
%T A301619 7937,8513,9281,9473,9857,10433,11393,11777,11969,12161,13121,13313,
%U A301619 13697,14081,14657,15233,15809,16001,16193,17729,17921,19073,19457,19841,21377,21569
%N A301619 Primes congruent to 65 (mod 192).
%C A301619 In other words, primes of the form 192*k+65 for k > 0.
%H A301619 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 A301619 Select[Prime[Range[2500]], MemberQ[{65}, Mod[#, 192]] &] (* _Vincenzo Librandi_, Jan 04 2020 *)
%o A301619 (PARI) forprime(p=1, 5e4, if(Mod(p, 192)==65, print1(p, ", ")))
%o A301619 (Magma) [p: p in PrimesUpTo(25000) | p mod 192 in {65}]; // _Vincenzo Librandi_, Jan 04 2020
%Y A301619 Subsequence of A002144 (primes of form 4*k+65) and A007519 (primes of form 8*k+65).
%Y A301619 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 A301619 nonn,easy
%O A301619 1,1
%A A301619 _Felix Fröhlich_, Mar 24 2018