A295243 Sums of two numbers that are both consecutive and squarefree.

3, 5, 11, 13, 21, 27, 29, 43, 45, 59, 61, 67, 69, 75, 77, 83, 85, 93, 115, 117, 123, 131, 133, 139, 141, 147, 155, 157, 165, 171, 173, 187, 189, 203, 205, 211, 213, 219, 221, 227, 229, 237, 245, 259, 261, 267, 275, 277, 283, 285, 291, 309, 315, 317, 331

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.

Intersection of 2*A005117+1 and 2*A005117-1. (End)

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

Cf. A005117, A007674, A065474.

Sequence in context: A329760 A156221 A207325 * A179017 A078971 A266723

Adjacent sequences: A295240 A295241 A295242 * A295244 A295245 A295246

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 18 2017

Status

approved