A358754 - OEIS

%I #13 Apr 16 2024 02:39:47

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 6m+1, otherwise a(n) = 0.

%H Antti Karttunen, <a href="/A358754/b358754.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.

%F a(n) = [A053669(n) == +1 (mod 6)], where [ ] is the Iverson bracket.

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime, p == 1 (mod 6)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.02897288485... . - _Amiram Eldar_, Apr 16 2024

%t a[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; Boole[Mod[p, 6] == 1]]; Array[a, 100] (* _Amiram Eldar_, Apr 16 2024 *)

%o (PARI)

%o A053669(n) = forprime(p=2, , if(n%p, return(p)));

%o A358754(n) = (1 == (A053669(n)%6));

%Y Characteristic function of A358756.

%Y Cf. A053669, A358755.

%Y Cf. also A353528.

%Y Differs from the characteristic function of A249674 for the first time at n=210, as here a(210) = 0.

%K nonn

%O 1

%A _Antti Karttunen_, Dec 03 2022