A089203 Primes p such that p-2 and p+2 are divisible by a fourth power.

169373, 371873, 574373, 741877, 843127, 979373, 1146877, 1615871, 1688123, 1754377, 1789373, 1855627, 2004833, 2093123, 2260627, 2498123, 2665627, 2700623, 2782757, 2903123, 3206873, 3374377, 3510623, 3560681, 3611873

Offset

1,1

Links

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

Example

169373 is a term since 169373 - 2 = 3^5*17*41 is divisible by 3^4 and 169373 + 2 = 5^4*271 is divisible by 5^4.

Mathematica

q1[n_] := AnyTrue[FactorInteger[n][[;; , 2]], # > 3 &]; q2[p_] := PrimeQ[p] && q1[p - 2] && q1[p + 2]; Select[Range[4*10^6], q2] (* Amiram Eldar, Mar 24 2021 *)

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", "); ) ); }
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: A034211 A308635 A210152 * A236054 A233801 A233802

Adjacent sequences: A089200 A089201 A089202 * A089204 A089205 A089206

Keyword

easy,nonn

Author

Cino Hilliard, Dec 08 2003

Status

approved