OFFSET
1,1
COMMENTS
From Robert Israel, Nov 20 2017: (Start)
All terms == 3 or 5 (mod 8).
Odd numbers k such that (k-1)/2 and (k+1)/2 are both squarefree.
The asymptotic density of this sequence is (1/2) * Product_{p prime} (1 - 2/p^2) = A065474 / 2 = 0.161317049469... . - Amiram Eldar, Feb 26 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 2*A007674(n) + 1. - Amiram Eldar, Feb 26 2024
EXAMPLE
a(3) = 11; 11 = 5 + 6, with 5, 6 consecutive and squarefree.
MAPLE
with(numtheory): a:=n->`if`(mobius(n)^2 = 1 and mobius(n+1)^2=1, 2*n+1, NULL): seq(a(n), n=1..300);
MATHEMATICA
Total /@ Select[Partition[Range@ 166, 2, 1], AllTrue[#, SquareFreeQ] &] (* Michael De Vlieger, Nov 18 2017 *)
PROG
(PARI) lista(nn) = for (n=0, nn, if (issquarefree(n) && issquarefree(n+1), print1(2*n+1, ", ")); ); \\ Michel Marcus, Nov 19 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Nov 18 2017
STATUS
approved