A358756 - OEIS

%I #16 Dec 05 2023 01:42:06

%S 30,60,90,120,150,180,240,270,300,330,360,390,450,480,510,540,570,600,

%T 660,690,720,750,780,810,870,900,930,960,990,1020,1080,1110,1140,1170,

%U 1200,1230,1290,1320,1350,1380,1410,1440,1500,1530,1560,1590,1620,1650,1710,1740,1770,1800,1830,1860,1920,1950

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

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

%C 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

%H Robert Israel, <a href="/A358756/b358756.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(n) local p;

%p   p:= 3;

%p   do

%p       p:= nextprime(p);

%p     if n mod p <> 0 then return (p mod 6 = 1) fi

%p   od

%p end proc:

%p select(filter, [seq(i,i=6..10000,6)]); # _Robert Israel_, Dec 04 2023

%t 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 *)

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

%Y Cf. A358754 (characteristic function), A358757.

%Y Cf. A002476, A053669, A358755.

%Y Cf. also A353528.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 03 2022