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.

A028877 Primes of form k^2 - 5.

This page as a plain text file.
%I A028877 #31 Feb 22 2025 14:46:01
%S A028877 11,31,59,139,191,251,479,571,1019,1151,1291,1439,1759,1931,2111,2699,
%T A028877 3359,4091,5179,5471,6079,6719,8831,10399,12539,13451,14879,17419,
%U A028877 20731,23099,26891,27551,28219,30271,30971,33119,33851,34591,35339,39199,41611,44939,49279
%N A028877 Primes of form k^2 - 5.
%C A028877 These numbers are prime in Z but not in Z[sqrt(5)] nor in Z[phi] (where phi is the golden ratio), since (k - sqrt(5))(k + sqrt(5)) = ((k + 1) - 2*phi)((k - 1) + 2*phi) = k^2 - 5. - _Alonso del Arte_, Aug 27 2013
%H A028877 Vincenzo Librandi, <a href="/A028877/b028877.txt">Table of n, a(n) for n = 1..8000</a>
%H A028877 Patrick De Geest, <a href="https://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics of the form n(n+x)</a>.
%H A028877 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>.
%F A028877 a(n) = A028875(A028876(n)). - _Elmo R. Oliveira_, Feb 22 2025
%e A028877 31 is in the sequence as it is equal to 6^2 - 5.
%e A028877 59 is in the sequence since it is equal to 8^2 - 5.
%e A028877 95 is not in the sequence though it does equal 10^2 - 5.
%t A028877 Select[Table[n^2 - 5, {n, 200}], PrimeQ] (* _Harvey P. Dale_, Jan 17 2011 *)
%o A028877 (Magma) [a: n in [1..300] | IsPrime(a) where a is n^2-5]; // _Vincenzo Librandi_, Dec 01 2011
%Y A028877 Cf. A028875 (superset), A028876.
%K A028877 nonn,easy
%O A028877 1,1
%A A028877 _Patrick De Geest_