A358756 Numbers k such that the smallest prime that does not divide them is of the form 6m+1.

30, 60, 90, 120, 150, 180, 240, 270, 300, 330, 360, 390, 450, 480, 510, 540, 570, 600, 660, 690, 720, 750, 780, 810, 870, 900, 930, 960, 990, 1020, 1080, 1110, 1140, 1170, 1200, 1230, 1290, 1320, 1350, 1380, 1410, 1440, 1500, 1530, 1560, 1590, 1620, 1650, 1710, 1740, 1770, 1800, 1830, 1860, 1920, 1950

Offset

1,1

Comments

Numbers k such that A053669(k) is in A002476.

The asymptotic density of this sequence is Sum_{p prime, p == 1 (mod 6)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.02897288485... . - Amiram Eldar, Dec 04 2022

Links

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

Maple

filter:= proc(n) local p;
  p:= 3;
  do
      p:= nextprime(p);
    if n mod p <> 0 then return (p mod 6 = 1) fi
  od
end proc:
select(filter, [seq(i, i=6..10000, 6)]); # Robert Israel, Dec 04 2023

Mathematica

f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; Select[Range[2000], Mod[f[#], 6] == 1 &] (* Amiram Eldar, Dec 04 2022 *)

Prog

(PARI) isA358756(n) = A358754(n);

Crossrefs

Cf. A358754 (characteristic function), A358757.

Cf. A002476, A053669, A358755.

Cf. also A353528.

Sequence in context: A226944 A249674 A050519 * A069819 A143207 A359410

Adjacent sequences: A358753 A358754 A358755 * A358757 A358758 A358759

Keyword

nonn

Author

Antti Karttunen, Dec 03 2022

Status

approved