A358849 Numbers k for which A053669(6*k) [the smallest prime not dividing 6k] is of the form 6m-1.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94

Offset: 1

Author

Antti Karttunen, Dec 03 2022

Keywords

• nonn

Comments

The asymptotic density of this sequence is 6 * Sum_{p prime, p == 5 (mod 6)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.8261626908... . - Amiram Eldar, Dec 04 2022

Examples

			35 is present as 6*35 = 210 = 2*3*5*7, and the first nondividing prime is 11, which is of the form 6m+5. This is the first multiple of 5 in this sequence.
385 is not present as 6*385 = 2310 = 2*3*5*7*11, and the first nondividing prime is 13, which is of the form 6m+1, not of 6m+5.
		

Crossrefs

Cf. A053669, A358847 (characteristic function), A358848 (complement).

Programs

Mathematica

f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; Select[Range[100], Mod[f[6*#], 6] == 5 &] (* Amiram Eldar, Dec 04 2022 *)

PARI

isA358848(n) = A358847(n);

Formula

{k | A053669(6*k) == 5 (mod 6)}.