Voozh

A380534

a(n) = 1 if the least significant nonzero digit in primorial base representation of n (A049345) is greater than 1, otherwise 0.

0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

COMMENTS

a(n) = 1 if A327860(n) [or equally, A329029(n)] is a multiple of A053669(n), otherwise 0.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Index entries for sequences related to primorial base.

FORMULA

a(n) = [A276088(n) > 1], where [ ] is the Iverson bracket.

a(n) = [A327860(n) == 0 mod A053669(n)].

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - A064648 = 0.294769828... . - Amiram Eldar, Feb 17 2025

MATHEMATICA

a[n_] := Module[{k = n, p = 2, r}, While[{k, r} = QuotientRemainder[k, p]; k > 0 && r == 0, p = NextPrime[p]]; If[r == 1, 0, 1]]; Array[a, 120] (* Amiram Eldar, Feb 17 2025 *)

PROG

(PARI)

A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };

A380534(n) = (A276088(n)>1);

(PARI)

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

A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };

A380534(n) = !(A327860(n)%A053669(n));

(PARI)

A329029(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); if(e, m *= (p^e); s += (1/p)); n = n\p; p = nextprime(1+p)); (s*m); };

A380534(n) = !(A329029(n)%A053669(n));

CROSSREFS