A089201 Primes p such that p-3 and p+3 are divisible by a cube.

683, 1747, 2659, 3253, 4253, 4397, 7253, 7549, 8747, 9829, 10253, 12253, 13037, 14747, 16253, 16747, 17747, 18253, 18637, 19891, 20747, 21269, 23747, 25253, 25747, 27253, 28123, 29501, 30253, 31253, 34253, 34603, 34747, 35747, 37253

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..330 from R. J. Mathar)

Formula

{p in A000040: p+3 in A046099 and p-3 in A046099}. - R. J. Mathar, Dec 08 2015

Example

683-3=2^3*5*17,683+3=2*7^3.

Maple

isA089201 := proc(n)
    if isprime(n) then
        isA046099(n-3) and isA046099(n+3) ;
    else
        false;
    end if;
end proc: # R. J. Mathar, Dec 08 2015

Mathematica

Select[Prime[Range[4000]], Max[Transpose[FactorInteger[#-3]][[2]]]>2 && Max[ Transpose[FactorInteger[#+3]][[2]]]>2&] (* Harvey P. Dale, Jan 26 2013 *)

Prog

(PARI) 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. A046099.

Sequence in context: A045154 A300193 A234502 * A292174 A065123 A269486

Adjacent sequences: A089198 A089199 A089200 * A089202 A089203 A089204

Keyword

easy,nonn

Author

Cino Hilliard, Dec 08 2003

Status

approved