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

1,1

Links

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

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. 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) } ispowerfree(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] >= p1, flag=0; break); ); return(flag) }

Crossrefs

Cf. A075432, A086708, A086709.

Sequence in context: A250904 A250948 A157433 * A023320 A206149 A221156

Adjacent sequences: A089209 A089210 A089211 * A089213 A089214 A089215

Keyword

easy,nonn

Author

Cino Hilliard, Dec 09 2003

Status

approved