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A089212 Primes p such that p-1 and p+1 are divisible by a fifth power.

%I A089212 #23 Sep 03 2024 15:02:35
%S A089212 13121,20897,25759,75329,80191,106433,118751,137537,153089,157951,
%T A089212 176417,191969,196831,207521,212383,215297,230849,243487,251263,
%U A089212 274591,281249,285281,313471,318751,321247,324161,331937,336799,347489,378593
%N A089212 Primes p such that p-1 and p+1 are divisible by a fifth power.
%H A089212 Amiram Eldar, <a href="/A089212/b089212.txt">Table of n, a(n) for n = 1..10000</a>
%e A089212 13121 is a term since 13121 - 1 = 2^6 * 5 * 41, 13121 + 1 = 2 * 3^8.
%t A089212 f[n_]:=Max[Last/@FactorInteger[n]]; lst={};Do[p=Prime[n];If[f[p-1]>=5&&f[p+1]>=5,AppendTo[lst,p]],{n,8!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 03 2009 *)
%o A089212 (PARI) \\ Input no. of iterations n, power p and number to subtract and add k.
%o A089212 ispowerfree(m,p1) = { flag=1; y=component(factor(m),2); for(i=1,length(y), if(y[i] >= p1,flag=0;break); ); return(flag) }
%o A089212 powerfreep4(n,p,k) = { c=0; pc=0; forprime(x=2,n, pc++; if(!ispowerfree(x-k,p) && !ispowerfree(x+k,p), c++; print1(x","); ) ); print(); print(c","pc","c/pc+.0) }
%Y A089212 Cf. A075432, A086708, A086709.
%K A089212 easy,nonn
%O A089212 1,1
%A A089212 _Cino Hilliard_, Dec 09 2003