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.

A056905 Primes of the form k^2 + 5.

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%I A056905 #25 Feb 16 2025 08:32:43
%S A056905 5,41,149,1301,2309,5189,6089,9221,13001,15881,26249,28229,39209,
%T A056905 41621,60521,66569,86441,112901,116969,138389,171401,186629,207941,
%U A056905 213449,242069,254021,266261,285161,304709,331781,345749,352841,389381,443561
%N A056905 Primes of the form k^2 + 5.
%C A056905 Except for a(0), a(n) mod 180 = 41 or 149 since k must be a multiple of 6 without being a multiple of 30 for k^2+5 to be prime.
%H A056905 Vincenzo Librandi, <a href="/A056905/b056905.txt">Table of n, a(n) for n = 1..1800</a>
%H A056905 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>
%F A056905 a(n) = 36 * A056906(n) + 5.
%e A056905 a(2)=149 since 12^2 + 5 = 149, which is prime.
%t A056905 Select[Table[n^2+5,{n,0,7000}],PrimeQ] (* _Vincenzo Librandi_, Nov 30 2011 *)
%o A056905 (Magma) [a: n in [0..700] | IsPrime(a) where a is n^2+5]; // _Vincenzo Librandi_, Nov 30 2011
%o A056905 (PARI) is(n) = ispseudoprime(n) && issquare(n-5) \\ _Felix Fröhlich_, May 25 2018
%Y A056905 Cf. A002496, A056899, A049423, A005473.
%K A056905 nonn,easy
%O A056905 1,1
%A A056905 _Henry Bottomley_, Jul 07 2000