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A089212
Primes p such that p-1 and p+1 are divisible by a fifth power.
6
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
1,1
LINKS
EXAMPLE
13121 is a term since 13121 - 1 = 2^6 * 5 * 41, 13121 + 1 = 2 * 3^8.
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 *)
PROG
(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) }
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Dec 09 2003
STATUS
approved