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.

A040119 Primes p such that x^4 = 10 has a solution mod p.

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%I A040119 #20 Jul 08 2025 22:48:54
%S A040119 2,3,5,31,37,41,43,53,67,71,79,83,107,151,163,173,191,199,227,239,241,
%T A040119 271,277,283,307,311,317,347,359,397,431,439,443,467,479,523,547,563,
%U A040119 587,599,613,631,641,643,683,719
%N A040119 Primes p such that x^4 = 10 has a solution mod p.
%H A040119 Vincenzo Librandi, <a href="/A040119/b040119.txt">Table of n, a(n) for n = 1..1000</a>
%t A040119 ok [p_]:=Reduce[Mod[x^4 - 10, p]== 0, x, Integers]=!= False; Select[Prime[Range[180]], ok] (* _Vincenzo Librandi_, Sep 12 2012 *)
%o A040119 (PARI) isA040119(p)={r=0;for(m=0,p-1,if(Mod(m,p)^4==Mod(10,p),r=1));r} \\ _Michael B. Porter_, Oct 13 2009
%o A040119 (PARI) select( {is_A040119(p)=ispower(Mod(10, p), 4)}, primes(199)) \\ is_A040119(p) assumes that p is prime, else append "&& isprime(p)". - _M. F. Hasler_, Nov 19 2024
%o A040119 (Magma) [p: p in PrimesUpTo(800) | exists(t){x : x in ResidueClassRing(p) | x^4 eq 10}]; // _Vincenzo Librandi_, Sep 12 2012
%Y A040119 Cf. A040121 (complement in the primes).
%K A040119 nonn,easy
%O A040119 1,1
%A A040119 _N. J. A. Sloane_
%E A040119 Definition corrected by _Michael B. Porter_, Oct 13 2009