A155141 - OEIS

A155141

Primes p such that both p-+4 are squarefree.

2, 3, 7, 11, 17, 19, 37, 43, 47, 61, 73, 83, 89, 97, 101, 107, 109, 127, 137, 163, 181, 191, 197, 199, 223, 227, 233, 251, 263, 269, 277, 281, 307, 313, 317, 331, 349, 353, 389, 397, 431, 433, 439, 443, 449, 457, 461, 467, 487, 523, 541, 547, 557, 569, 577, 587

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OFFSET

1,1

COMMENTS

The numbers of terms that do not exceed the (10^k)-th prime, for k = 1, 2, ..., are 6, 51, 532, 5349, 53500, 534963, 5351408, 53510238, 535103289, 5351081043, ... . It appears that the relative asymptotic density of this sequence within the primes exists and equals Product_{p odd prime} (1-2/(p*(p-1))) = 0.535107012... (A271780). - Amiram Eldar, Aug 20 2026

LINKS

John Cerkan, Table of n, a(n) for n = 1..10000

MATHEMATICA

lst={}; Do[p=Prime[n]; If[SquareFreeQ[p-4]&&SquareFreeQ[p+4], AppendTo[lst, p]], {n, 6!}]; lst

(* Alternative: *)

Select[Prime[Range[150]], AllTrue[#+{4, -4}, SquareFreeQ]&] (* Harvey P. Dale, Jun 15 2016 *)

PROG

(PARI) lista(nn) = forprime(p=2, nn, if (issquarefree(p-4) && issquarefree(p+4), print1(p, ", "))); \\ Michel Marcus, Jul 06 2016

CROSSREFS

Cf. A153213, A049282, A155139, A155140, A155142, A271780.

Sequence in context: A394450 A235482 A375818 * A127944 A294677 A274161

Adjacent sequences: A155138 A155139 A155140 * A155142 A155143 A155144

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

STATUS

approved