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A162876 Twin prime pairs p, p+2 such that p-1 and p+3 are both squarefree. 1
3, 5, 11, 13, 59, 61, 71, 73, 107, 109, 179, 181, 191, 193, 227, 229, 311, 313, 419, 421, 431, 433, 599, 601, 659, 661, 827, 829, 1019, 1021, 1031, 1033, 1091, 1093, 1319, 1321, 1427, 1429, 1487, 1489, 1607, 1609, 1619, 1621, 1787, 1789, 1871, 1873, 1931 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By definition, the lower member, here at the odd-indexed positions, is in A089188.

p+1 must be divisible by 4. - Robert Israel, Jul 24 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

{(p,p+2) : p in A001359, and p-1 in A005117, and p+3 in A005117}.

EXAMPLE

(179,181) are in the sequence because 179-1=2*89 is squarefree and 181+1=2*7*13 is also squarefree.

MAPLE

f:= p -> if isprime(p) and isprime(p+2) and numtheory:-issqrfree(p-1) and numtheory:-issqrfree(p+3) then (p, p+2) else NULL fi:

map(f, [4*k-1 $ k=1..1000]); # Robert Israel, Jul 24 2015

MATHEMATICA

f[n_]:=Module[{a=m=0}, Do[If[FactorInteger[n][[m, 2]]>1, a=1], {m, Length[FactorInteger[n]]}]; a]; lst={}; Do[p=Prime[n]; r=p+2; If[PrimeQ[r], If[f[p-1]==0&&f[r+1]==0, AppendTo[lst, p]; AppendTo[lst, r]]], {n, 7!}]; lst

CROSSREFS

Cf. A089189, A089194, A162870, A162872, A162873, A162874, A162875

Sequence in context: A006794 A032457 A122564 * A162875 A166564 A058595

Adjacent sequences:  A162873 A162874 A162875 * A162877 A162878 A162879

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 15 2009

EXTENSIONS

Definition rephrased by R. J. Mathar, Jul 27 2009

STATUS

approved

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Last modified April 14 05:21 EDT 2021. Contains 342943 sequences. (Running on oeis4.)