|
Search: id:A089194
|
|
|
| A089194 |
|
Primes p such that p-1 and p+1 are cube- or higher power-free. |
|
+0
7
|
|
| 2, 3, 5, 11, 13, 19, 29, 37, 43, 59, 61, 67, 83, 101, 131, 139, 149, 157, 173, 179, 181, 197, 211, 227, 229, 277, 283, 293, 307, 317, 331, 347, 349, 373, 389, 397, 419, 421, 443, 461, 467, 491, 509, 523, 547, 557, 563, 571, 587, 613, 619, 643, 653, 659, 661
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
EXAMPLE
|
43 is included because 43-1 = 2*3*7 and 43+1 = 2^2*11 are both cube-free.
71 is omitted because the p+1 side, 72 = 2^3*3^2, has a cube factor.
|
|
MATHEMATICA
|
f[n_]:=Module[{a=m=0}, Do[If[FactorInteger[n][[m, 2]]>2, a=1], {m, Length[FactorInteger[n]]}]; a]; lst={}; Do[p=Prime[n]; If[f[p-1]==0&&f[p+1]==0, AppendTo[lst, p]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 15 2009]
|
|
PROGRAM
|
(PARI) \input number of iterations n, power p and the number to subtract k. powerfreep2(n, p, d) = { c=0; pc=0; forprime(x=2, n, pc++; if(ispowerfree(x-d, p) && ispowerfree(x+d, 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
|
Sequence in context: A104293 A153002 A042999 this_sequence A050229 A053184 A020607
Adjacent sequences: A089191 A089192 A089193 this_sequence A089195 A089196 A089197
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Dec 08 2003
|
|
|
Search completed in 0.002 seconds
|
