login
A358847
a(n) = 1 if A053669(6*n) [the smallest prime not dividing 6*n] is of the form 6m-1, otherwise a(n) = 0.
5
1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0
OFFSET
1
FORMULA
a(n) = A358755(6*n).
a(n) = A358846(n-1) XOR A358846(n), where XOR is bitwise-XOR, A003987. See comments in A358755.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 6 * Sum_{p prime, p == 5 (mod 6)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.8261626908... . - Amiram Eldar, Apr 16 2024
EXAMPLE
For n = 85085 = 5*7*11*13*17, 6*n = A002110(7) = 510510, whose smallest nondividing prime is 19, which is of the form 6m+1, therefore a(85085) = 0.
For n = 1616615 = 5*7*11*13*17*19, 6*n = A002110(8), whose smallest nondividing prime is 23, which is of the form 6m-1, therefore a(1616615) = 1.
For n = 37182145 = 5*7*11*13*17*19*23, 6*n = A002110(9), whose smallest nondividing prime is 29, which is of the form 6m-1, therefore a(37182145) = 1. This is the first case where the alternating pattern following A276084 breaks.
PROG
(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p)));
A358847(n) = (5 == (A053669(6*n)%6));
(PARI) a(n)=forprime(p=5, , if(n%p, return(p%6==5))) \\ Charles R Greathouse IV, Dec 03 2022, corrected by Antti Karttunen, Apr 14 2024
CROSSREFS
Characteristic function of A358849, whose complement A358848 gives the positions of zeros.
Cf. also asymptotics of A353528 and A353529.
Sequence in context: A099443 A132342 A156174 * A187967 A106467 A106468
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Dec 03 2022
STATUS
approved