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 A295243 Sums of two numbers that are both consecutive and squarefree. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 9 10:46 EDT 2024. Contains 375764 sequences. (Running on oeis4.)