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A272799 Numbers n such that 2n - 1 and 2n + 1 are squarefree. 3
1, 2, 3, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 33, 34, 35, 36, 39, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 64, 65, 66, 69, 70, 71, 72, 75, 78, 79, 80, 81, 82, 83, 89, 90, 91, 92, 93, 96, 97, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 110 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

a(n) = (A069977(n)+1)/2. - Charles R Greathouse IV, May 15 2016

EXAMPLE

a(1) = 1 because 2*1 - 1 = 1 is squarefree and 2*1 + 1 = 3 is squarefree.

MAPLE

Res:=  NULL: count:= 0: state:= 1;

for n from 1 while count < 100 do

  if numtheory:-issqrfree(2*n+1) then

    if state = 1 then Res:= Res, n; count:= count+1;

    else

      state:= 1;

    fi

  else

    state:= 0;

  fi

od:

Res; # Robert Israel, Apr 15 2019

MATHEMATICA

Select[Range[12^4], And[Or[# == 1, GCD @@ FactorInteger[#][[All, 2]] > 1], SquareFreeQ[# - 1], SquareFreeQ[# + 1]] &] (* Michael De Vlieger, May 08 2016 *)

PROG

(MAGMA) [n: n in [1..110] | IsSquarefree(2*n-1) and IsSquarefree(2*n+1)];

(PARI) is(n)=issquarefree(2*n-1) && issquarefree(2*n+1) \\ Charles R Greathouse IV, May 15 2016

CROSSREFS

Cf. A069977, A226993.

Sequence in context: A050023 A047505 A039071 * A300157 A265334 A050019

Adjacent sequences:  A272796 A272797 A272798 * A272800 A272801 A272802

KEYWORD

nonn,easy

AUTHOR

Juri-Stepan Gerasimov, May 06 2016

STATUS

approved

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Last modified August 10 16:56 EDT 2020. Contains 336381 sequences. (Running on oeis4.)