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

13121, 20897, 25759, 75329, 80191, 106433, 118751, 137537, 153089, 157951, 176417, 191969, 196831, 207521, 212383, 215297, 230849, 243487, 251263, 274591, 281249, 285281, 313471, 318751, 321247, 324161, 331937, 336799, 347489, 378593

Offset: 1

Author

Cino Hilliard, Dec 09 2003

Keywords

• easy
• nonn

Examples

			13121 is a term since 13121 - 1 = 2^6 * 5 * 41, 13121 + 1 = 2 * 3^8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A075432, A086708, A086709.

Programs

Mathematica

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 *)

PARI

\\ Input no. of iterations n, power p and number to subtract and add k.
ispowerfree(m,p1) = { flag=1; y=component(factor(m),2); for(i=1,length(y), if(y[i] >= p1,flag=0;break); ); return(flag) }
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) }