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A089203 Primes p such that p-2 and p+2 are divisible by a fourth power. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 20:35 EDT 2022. Contains 355994 sequences. (Running on oeis4.)